All the advice above is good. But it's your body, and your pain, so make sure it's not a chronic issue.
First, consider doing some work on your forearm flexors, so that they get a chance to strengthen at a pace similar to your goals for your biceps and brachii. Since going back to heavy lifting, my forearms and my grip have needed serious work to keep up, and it can be very frustrating, but in time, it resolves. It should resolve for you, too. Until then, Em3ns advice is very sound.
However, if it's chronic, meaning it applies to time outside the gym, for instance when you are doing normal gripping and lifting activities that don't involve heaver resistance, then get it looked at by a doctor. Don't panic, but don't wait.
As helpful as all of us are trying to be, the reality is that nothing can be diagnosed over the web, not even "oh, my arm does that, too". I want to emphasize that preventative medicine is less costly than emergency surgery. (I tore my distal biceps tendon off the bone two years ago, just bowling...and it actually had started with a small tear which I should have recognized at least two years prior...not working out, not treating it lead to something major that could have been avoided. I could have strengthened rather than further weakened it, and worked around it while it healed....but I didn't)
I have to assume that one of the reasons you're on RJ is that you take your workouts seriously. So, if a paid professional athlete has every little pull and pinch examined, what you're describing deserves a quick trip to your MD, at the very least, if it continues.