Fatter tires are irrelevant.

I developed an ulnar neuropathy from riding (with 35mm tires) and saw a neurologist about it. The first thing to do is change your hand position. You may want to get a professional fit as your bar width and stem combination might not be working for you. The second thing to do is sleep with your hands below your waist. Your arm needs the full extension during it's rest period. If your hands are under your head or on your chest, your sleep habits contribute to your problems on the bike.

EDIT: I am not qualified to make a diagnosis. I am only relating what my neurologist told me. See a neurologist, preferably one who has experience with sports-related injuries.