Edit: You have carpal tunnel likely because you're holding the pen/pencil incorrectly and exerting far too much pressure. Drummers have this problem too when they use the tiny muscles in their hand to do the job of the big muscles.
Check if you're holding your writing utensil correctly.
As a left handed person in China, I always get stairs when people see me writing with my left hand (like I was an alien?), and I have trouble eating at tightly packed circular tables.
I'm angry that I have carpal tunnel syndrome. Maybe I'd be less angry if I'd been trained to write using the Palmer Method.