Where is the pain located, i.e. is it on the ulnar-sided (pinky side) or radial-sided (thumb side)? Is it continuous or just when you do curls? What exercises hurt your wrists/forearms the most? These questions should help in figuring out what the problem is and ways to avoid similar ones in the future.
A general suggestion is to start using the ez-curl bar. Straight bb curls put a lot of stress on your wrists which can lead to tendonitis.
Taping your wrists, while good a quick-fix is just covering up the problem. It would be best if you cut out the exercises that hurt it for a couple weeks. Add in plenty icing and/or contrast bathing and they should heal fine. You can do heavy close-grip chins and rows to keep up your bicep strength/size, granted that such exercises don't hurt your wrists.
After its healed read these:
Probably, the only exercise you need from the second one it the plate-wrist curls.
At first, keep the weight low and reps high (15-20). Eventually, you can add weight and lower the reps.