Is it possible to get carpal tunnel from masturbation?

Sure. Many times the exact cause of carpal tunnel is not determined...Some people just get it. Some repetitive activities can cause swelling within the tendons of your carpal tunnel, which may increase pressure on the nerve involved. This may relate to frequency/duration of masturbation. Stop masturbating and see if your symptoms improve.
Probably. Try a different grip. This is good advice for everybody. By masturbating, you're learning about your body to prepare you for relationships, and you'll want to be familiar and good at responding to a variety of types of stimulation.