Bill will probably give you some good scientific and practical advice, but I'll chime in ahead of him anyway

I've had this particular pain several times.
1. Take a week off if you haven't in the last 8-12.
2. Stop isolating the small muscles (biceps and triceps) for at least a month. Concentrate on the larger ones (chest and back) by doing bench presses, dips (feet back - leaning forward), pullups, bent rows, etc.
3. See a doctor if it doesn't subside after the previous two steps.
My guess is that it's connective tissue not growing as fast as the muscles in your arms (well known fact that muscle grows faster) and is therefore under strain and causing pain.. When I've had it, I've done the above and been just fine. I usually take 6-12 weeks off of isolation exercises and then I can come back just fine. You'll have to figure out what works for you.