What is the solution to the obsessive thoughts about worshipping the Messenger, or believing that Allah has a son, or that Allah's names are exclusive to Jesus or Muhammad?

The solution to intrusive thoughts (waswas) is to ignore them and not pay attention to them. Your aversion to them is a sign of sincere faith, and they do no harm as long as your soul dislikes them. You must strive against them by saying "I believe in God" (Amantu billah) and by ceasing to think about them. The Muslim will be rewarded for this struggle and for their effort to get rid of them.