The answer to your question is it depends on why it hurts. If you have muscle cramps because you are using muscles you haven't used much before, then rest, heat (or cold) and NSAIDS and gradual building up of those muscles will work. You may have to cut down on the amount of time you sew at a time (down to 1 or 2 hours).
If you have a dull ache, sharp pain or numbness or tingling you probably have a repetitive motion injury (carpal tunnel or tennis elbow are 2 examples) and you have some part of your hand/wrist inflamed and its causing pressure on a nerve. Again, you must rest it to allow for the swelling to go down, and NSAIDS and ice can do wonders.
In either case, you may find a brace helps you avoid over-stressing the part of your wrist or hand that is getting hurt.
I would recommend seeing a MD and letting he or she diagnose you, and seeing a physical or occupational therapist who specializes in hand issues. I won't poo-poo chiropractors, I have met a few who were really skilled at manual therapy, I will tell you that not all are equal and a few are borderline charlatans, so get a referral and look for someone with a good reputation. I would personally choose an upper extremity specialist therapist over a chiro, but that's probably because I am a therapist myself. :)
Beth
(aka occupational therapist)