What is the ruling on doubting the transmission of impurity by pre-seminal fluid (wady) to underwear, the nose, towels, and hands, and subsequently to objects touched thereafter? And what is the correct action in these cases, especially with the affliction of obsessive-compulsive disorder and the refusal to take medication?

You must act according to the correct decision you made regarding performing istinja' (ablution after defecation/urination) without squeezing. You can also resort to sprinkling water on your trousers after istinja' to account for any perceived possibility of impurity dripping onto them. If you have performed istinja' and sprinkled water, then move on and do not pay attention to any obsessive thoughts you experience, for obsession is a serious illness, and its cure is to disregard it and not pay attention to it. You should also continue to consult doctors and take medications. What you might not know is that if someone finds impurity on their garment, they are not obliged to change it or perform ghusl (full ritual bath); rather, it suffices to wash the spot of impurity and perform wudu' (ablution) if the impurity appeared after performing wudu'. If you doubt whether you have been afflicted by impurity, the default is purity until you are certain of the impurity. Istinshaq (sniffing water into the nose) during ghusl is recommended, and doubting whether you omitted it after completing ghusl does not cause harm. Some scholars permit leniency regarding a small amount of impurity, and there is no harm for someone suffering from obsessive thoughts to act upon this view. If something exits from either of the two private parts and you are certain of its exit, then wudu' must be repeated.