What is the ruling on my suffering from recurring blasphemous and infidel thoughts, including insults to Allah and His Messenger, which never leave me at any time, and which I cannot get rid of despite my attempts?

Ugly (repugnant) whisperings are not of a person's doing, and they will not be held accountable for them. They are closer to psychological illnesses like obsessive-compulsive disorder. The person afflicted by them will be rewarded for striving against them and for their abhorrence of them. It is recommended to stop these whisperings and completely turn away from them, living a normal life without hardship in purification (tahara) or other things the person suffering from whisperings might imagine. There is no objection to consulting a religious psychiatrist who possesses both religious and medical knowledge.