I often have the same problem. I've had problems with tendonitis for years and, upon asking my doctor, he said many people who lift weights will experience some form of tendonitis/carpal tunnel/tendonosis (repetitive motions, overuse, etc.)...having the pre-existing condition hasn't made my workouts easy (not like they're supposed to be...but you get what I'm saying).
Using some joint cream (theragesic, icy hot) is a great way to sooth symptoms. If pain still persists, take 1 or 2 NSAIDs. Of course, resting the afflicted area is the best way to for it to heal. You can always talk to a trainer at your gym for help on bicep exercises that you can substitute when the inflammation occurs. Good luck!