It depends. If your problem comes from doing too much with the hand in the first place, doing exercises right now could actually make things worse. Exercises that cause the wrist to bend can put more pressure around the median nerve inside the carpal tunnel. If your symptoms are coming from extra pressure, you might need to wear a splint to rest your wrist and fingers. When your symptoms calm down, exercises can improve movement and strength.
Used in the 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 carpal tunnel syndrome. When symptoms have gone 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.