Is the questioner's action of not paying attention to the doubt about his clothes becoming impure correct, and did everything these clothes touched become impure if they were impure?

You are afflicted with Waswasah (obsessive doubts), and the optimal treatment for it is to ignore it. The fundamental principle is that ritual impurity (najasa) is not transferred. Therefore, if you doubt whether your body or clothing has become impure, the certainty is purity, and this certainty cannot be superseded except by a certainty of equal strength. Your disregard of these doubts is correct, and all your prayers are valid.