Is it obligatory to dispose of wristwatches purchased after seeing a picture of Prophet Jesus (peace be upon him) in a shop, given the feeling that the watches may have become impure because of it, and will this "impurity" transfer to everything bought while wearing them?

It is impermissible to depict prophets, especially if the images are three-dimensional, due to the Prophet's (peace and blessings be upon him) saying: "The most severely punished people on the Day of Resurrection will be the image-makers." And seeing forbidden images has no relation to what a person buys on that day. It is advisable to abandon obsessive thoughts and pessimism, for there is no impediment to wearing watches, selling them, giving them in charity, or gifting them.