To answer the above question in detail from a Shari'ah perspective, we need to make mention of general points at first. Thereupon, we will elaborate on Shari'ah perspective or issues which we shall deal with separately.
1. There are different verses in the Quran which denote that there is no hardship in religion:
وَ مَا جَعَلَ عَلَيْكُمْ فِى الدِّينِ مِنْ حَرَج.
"He has chosen you and has not laid upon you an hardship in religion."[1]
The Holy Prophet (S) has said in a well-known tradition that he was sent to humanity with an easy and straight forward religion.[2] What is inferred clearly and decisively from the verses and prophetic tradition, as also stressed by prominent scholars in their jurisprudential arguments, is that if our understanding of the religion goes towards a direction which results in disrupting our daily lives and make it difficult, we must know then that such an understanding and perception, is different from what the Prophet (S) has taught us.  Hence, if a person feels that if he ought to maintain purity he will have to deprive himself of recreation and beauties of life, he must know for sure that since such a self-imposed restriction amounts to undergoing hardship and difficulty in life, it is definitely against Islam's instruction concerning purity and cleanness. Even if the rules of cleanness do not change, wherever the duty-bound faces extremely difficulty as a result of abiding by them, the rules become null and void.[3]
2. The commandments of Islam have been revealed and explained in the language of the people of the Arabians in the early period of Islam. Back then, few people could read and write and many people never paid attention to rational accuracy.  Therefore, to act upon such commandments, we should know what the Arabs of that time understood from them. How were they conducting themselves?  Definitely, they were not as much particular about cleanness and uncleanness as an educated individual. A chemist knows that the particles of a liquid constantly spread in the air and these tiny particles definitely settle on the objects around them. In this case, does Islam rule that any object which is near an impure liquid becomes unclean?  The answer is definitely in the negative. However, we do know that a very small quantity of the unclean liquid has settled on nearby objects. In such an example, there is no doubt that according to all the ordinary people of the early period of Islam, as well as the people of the present time, the liquid inside the container has not spread on to the surrounding objects, although from a meticulous scientific perspective, something from the liquid has spread but the Divine Legislator rules on the basis of ordinary people's view. That is, things which are made unclean as a result of some unclean liquid spreading to it, are treated as unclean, not things which may get affected on account of meticulous rational point of understanding.[4]
3. Some of the things which people with obsessive compulsive disorder believe should do result in committing forbidden acts such as extravagance and wastefulness (isfraf), insulting religion, severing relations, breaking off with close relatives or with other Muslims and accusing others of immorality and indecency. If we assume that the obsessive people's argument is correct and logical, since it leads to great sins, it should be left aside because the religion of Islam says that  we should do what is more important than that which is less important. That is, if we compare the rules regarding purity and wasting of time and water, the rules regarding purity should be left aside and that the rules about preventing the wastage of these two capitals take precedence. Similarly, if implementation of a jurisprudential rule causes someone to be cast out or isolated in community, since the Shari'ah does not consent to it, definitely, the rules regarding purity are put aside.  Given the fact that observance of purity is not among the important and main rules, this comparison is extended to all the rules and must be taken into consideration.
4. Despite these guidelines, some people are excessively obsessed with Shari'ah issues. They end up suffering from OCD.  Religious authorities have enumerated special rules for these people. At times the rules they have to follow are different from the rules which have to be followed by others.  Considering that scrupulousness and obsession in religious issues come into being for those who are adherent to Shari'ah rules or commandments, the same people should follow Shari'ah rules without indulging their own personal views and internal inclination. Thus, they should submit themselves to what Islamic Shari'ah says to them. Late Imam Khomeini says, "A person suffering from OCD must not pay heed to his doubts and if he does so, he has committed a haram deed. He should not do every action more than once and if he does so, he has committed a haram action."[5] This clear edict shows that following one's obsession in religious issues not only isn't considered to be adherence to the commandments of Allah but it also a sin which entails divine punishment. In a saying of late Sayyid Muhammad Kazim Yazdi, the author of 'Urwat al-Wuthqa, the most famous book in jurisprudence in the Islamic Seminary, says: "An obsessive person's knowledge has no value."[6] This statement means that a person who is suffering from obsessive compulsive disorder must not act upon his own knowledge of something. If he is certain that something is impure, his certainty does not mean that the thing which he is certain to be impure is really impure. That is to say, he can pray with it and if it is an edible, there is no objection to him eating it. This rule is applicable to all jurisprudential issues (more details to come in the second section of this answer).
Those who end up suffering from obsessive compulsive disorder owing to excessive scrupulousness towards Shari'ah obligations, understand in view of the foregoing details which are quite demonstrative and solid that the method they have adopted to comply divine orders is incorrect and shall not earn the pleasure of Allah.
Now coming to your special problem which relates to the rules of purity, we have several separate points to mention:
1. Uncleanness of things:
a) Certainty in regards to things becoming impure as a result of coming in contact with impurity means that the individual can never consider it probable or create a probability in his mind that the two things have not come in contact with each other.[7]
b) An object which we are sure to be impure must be in such a way that the impurity which has reached it must have been through moisture from or to it. That is, we must be hundred percent sure that the moisture is to the extent that liquid, not chill, has passed from one object to another.[8]
c) Impurity does not pass to a wet object. In case, there is water at a place where there is impurity, it transfers the impurity.[9] In fact, even in this case, the impurity passes only when we are certain that the place where there is the impurity is not lower than other objects. That is to say, if water moves from clean places down to the najis area, the pure areas do not become impure. Even if there is a meager probability that impurity might have passed, such a probability is not heeded and the impurity is treated as not having passed.[10]
d) Things which we know they are sometimes clean and other times unclean such as the floor of a public toilet which is often washed with kurr water and at times they become unclean, as long as we are not sure that it has been made unclean now, we should treat it as clean and we are not at all supposed to avoid it.
Keeping the foregoing details into consideration, it becomes clear that if we are living with people who are careless about impurity or in case we are going to public places which we are not sure to be impure, we should consider everything as clean because it is very difficult to be sure that a certain object is impure.  We repeat that if we were aware of the reality, we would know that almost all the things around us are impure but God has made all of them pure for us. He has not made us to do anything about them. Indeed, if we know for sure that something is really impure, then we have to avoid it.
e) When it comes to a number of impure objects coming in contact with one another i.e. the first impure object comes in contact with another object and that object comes in contact with a third, Ayatollah Khamenei says, "Impurity does not pass to the fourth object onward. That is, after the fourth object comes in contact with the third najis (impure) object, the fourth object does not become impure."[11] As well, Imam Khomeini has said: "Impurity does not pass, if the things in the chain of objects are many."[12] Some other scholars are of the view that impurity does not pass from multiple objects to one another, if it causes hardship and difficulty.[13] Thus, it becomes clear that there is no reason to worry when you walk in a street covered with snow. That is because what we think to be transferring impurity to us is an intermediary which is far away from the original impure object which, according to some scholars, does not transfer the impurity or it does not make other things impure because of the difficulty it causes. As you have also pointed out in the question, it becomes very difficult and sometimes impossible to observe cleanness. Therefore, there remains no doubt that according to the verdict of scholars who have exercised precaution, again impurity does not pass to another object.
2. Purifying impure things
Religious scholars and jurists say that those who have obsession regarding cleanness should conduct themselves in the same way as other people even if they themselves do not become certain.[14] That is to say, if an obsessive individual does not become certain of the purity of a piece of clothes kept under tap water for half a minute, then since ordinary people suffice to this much time considering the impure object as pure, the impure object which the obsessive individual wants to purify will become pure, if it is kept under tap water for half a minute. Considering Imam Khomeini's verdict, washing something again and again and excessive precaution are not only unnecessary but it is also haram.
When it comes to using washing machines, we should mention that washing machines are of two types: "Those which spin the clothes while connected to kurr water and those which spin the clothes after the water is disconnected. The religious authorities have said in regards to the first case type that since kurr water reaches the clothes and the machine itself while spinning, both the machine and the clothes are made pure. In regards to the second type of washing machines, some religious authorities such as late Grand Ayatollah Bahjat have said that obligatory precaution has to be exercised.[15] And some scholars like Ayatollah Makarem Shirazi have reiterated that the clothes which are washed in a washing machine are made pure irrespective of whether the washing machine is connected to water or the water is disconnected.[16] For this reason, the followers of those scholars who have the same verdict as that of Ayatollah Bahjat can refer to Ayatollah Makarem Shirazi keeping in view the rules of Taqlid.[17]
When it comes to purifying things, we draw your attention to this point that according to the verdicts of religious authorities, if someone who possesses something says that it is clean and pure, that thing is treated as pure.[18] This shows that even if a carefree person says that something is pure, the cleanness of that object is proved. Religious scholars also say that if a Muslim individual rinses something, the cleanness of that thing is established, even though it is not known whether he has rinsed it correctly or not.[19] In view of this easy rule, why do we need to look for any other method whether or not the methods used for purifying things are correct or not.
In view of the above, one who acts upon Islamic injunctions which have reached us through jurisprudents, his actions will not end up in obsession. What actually results in obsession is a lack of insight and knowledge of the rules. Now that the rules have been clarified to some extent, we would offer two suggestions:
Firstly, the most important and most effective way to get rid of obsession is that he who is suffering from obsessive compulsive disorder must not be very particular and sensitive about purity or impurity of things he has to deal with. He should not do something over and over again putting himself in unnecessary trouble until he becomes certain and gets relieved of doing something since the obsessive compulsive disorder tends to increase and get worse because each time you feel that, for example your clothes and appliances are completely clean, the next time this feeling gets one step harder than ever before. Thus, it is necessary to advance on the opposite direction. If for now you do not want your husband's young sister touch you with her wet  hand but if there is no way you can avoid and you will have to put up with it by offering prayers with the moisture transferred to you from her, then this is the point where you are fighting obsessive compulsive disorder.  You should keep doing the same and if you have time to wash yourself, you should delay your obsession a little by not washing yourself and disengaging your mind. This has to be done gradually. For example, the same practice should be repeated at least for twenty times until one feels that he is no longer sensitive towards this situation.  Your sensitivity is thus delayed and lessened to some extent. For example, if you believed as of now that the bathroom floor is impure, you will, after one or two months, begin to entertain doubt about it being impure. Now do the previous action with your present sensitivity. You should note that you should fix the limit that when you have an extended period of time, you consider it as impure otherwise when you are in a hurry ignore it.
Secondly, since an obsessive individual may get some sort of impression from another obsessive individual as he might compare himself with him and believe his actions are ordinary; therefore it is necessary for him to avoid the company of obsessive people. He should stay away from them and should have no communication with them. If he is required to communicate with them, he suffice only to the necessary extent.
In conclusion, since obsessive compulsive disorder tends to aggravate and grow more intense, if this article does not address your problem completely, we advise you to refer to health professionals, psychologists and psychiatrists immediately to solve the problem. Do not consider stopping your efforts to get rid of the problem because, if you do so, it will have grave consequences.

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