I had this and was able to get rid of it. Basically it's tendonitis or similar, all caused by repetitive motions that create strain. A typical combo that cause this is pulling exercises that involve biceps and back work.
You have to remove the stress by trying variations of what you're doing, sometimes very minor changes make a difference. Wraps might also help in removing some of the stress, they might work in conjunction with finding more comfortable grips. Working through anything other than minor pain isn't practical long-term. If the pain's pronounced it's worth stopping any exercises that cause direct pain for a while, until some degree of healing occurs.
It's worth trying variations in grips using any number of different bars-E-Z curl, hammer-grip, DBs instead of BB, etc. Also to try using pulley versions of the exercises-the value of pulleys is (1) the stress comes from different angles that stress the areas differently, and (2) with pulleys you have a wider variety of handles and rope attachments that can be used to change the angle of the forces that are exerted. By trying different angles and different grips, the pain can fade away over time-standing pulley curls for example, are a good alternative to BB curls and may not stress the forearms as much. In my case it only took a minor change in grip to make a big difference, you have to try variations and see what the difference is.
Eventually if you don't get rid of it, you can get a cortizone shot from a doctor, which will remove the pain. Very effective. However if you don't remove the actual cause of the problem and find a better alternative in each case of problems, the pain will return eventually.
