It depends. If your problem is from doing too much with the hand in the first place, doing extra exercises right now could actually make things worse. Doing exercises that cause the wrist to bend can put more pressure around the median nerve inside the carpal tunnel. If symptoms are coming from extra pressure, you might need to wear a splint to help rest your wrist and fingers. When symptoms calm down, exercises can be done to improve movement and strength.
Addressed in early stages of the problem, exercises are one strategy to help prevent the problem from getting worse. However, it is not clear whether exercise alone can prevent or reverse problems of CTS. When symptoms have been going on long enough to cause the muscles on the thumb-side of the palm to atrophy (shrink in size), it’s likely that exercises will not correct the problem.