Is one who drives without a license sinful if he suffers from obsessive-compulsive disorder that prevents him from obtaining it, given his proficiency in driving and his dire need for it for his worldly and religious affairs?

You should consult a trusted psychiatrist to confront obsessive thoughts. The treatment for obsessive thoughts is to ignore them, for learning to drive is not difficult. You must adhere to the state's regulations that serve the public interest and do not contradict Islamic law, such as traffic laws, because violating them leads to accidents and inconvenience for others. No one is permitted to violate traffic laws, and rely on Allah to dispel obsessive thoughts.