Every time I go to the driving range, my forearms get sore. I had the same problem when I started throwing too many hard punches on the bag. That might be what's hurting you. Your first step should be to get a pro to observe your swing and make sure your form is good.
Golf requires finesse.
You don't want to get musclebound. Bending the wrist, lower the weight toward the floor. Open the fingers slightly so the weight rolls down the palm. Close the fingers and curl the weight up again. Work up to three sets of 10 each, two or three times a week.