I too ran into your problem, with my right elbow. Is the pain a dull pain...versus a sharp one? I traced my problem to what they call "Golfers Elbow". This is where you strain/damage the ligaments between the elbow and the foream muscles.
What worked for me is to ice down elbow after a work out, and Motrin every know and then when it was really nagging me. The best way to avoid this is NOT to do a full extension, i.e. if you are doing a curl, do not straighten your arm all the way down before doing the next curl...keep it slightly bent...and do this for any and all exercises that involve the elbows and foreams.
Also, work out the forearms with
wrist curls and
reverse wrist curls. I rarely have a problem anymore, and this is about all you can do for it. It will eventually go away if you try the above...and wrapping during a work out and after helps as well.