Is what the questioner does—closing the urethral opening when performing istinja' (washing after defecation or urination) to prevent water from entering it—correct? And do undergarments become impure if they touch the urethral opening after istinja'?

One afflicted with waswasah (whispers of Satan or obsessive doubts) should treat it by ignoring these whispers and not paying attention to them. For istinja (definition)' (cleaning oneself after relieving oneself), it is sufficient to pour water on the impure area until one is reasonably certain that the impurity has been removed. One should not pay attention to doubts about water entering the male organ. The water remaining on the male organ after purification is pure. The method described in the question is not prescribed by Islamic law; it involves excessive effort and tanattu' (being overly meticulous beyond what is required). Washing the outer part of the male organ is sufficient. Clothes that touch the male organ after istinja' are pure. One must use only the necessary amount of water without being extravagant.