If you are talking about the tendon in your forearm that attaches to the knobby bone on the inside of your elbow, i used to have the same problem. Mine hurt right where it attached to the knobby bone.
In my opinion, this likely happens because that tendon is recieving a lot of stress where it has not before. It might not be as relilliant as other tendons.
What i did was quit doing any pulling for about 3 weeks (not even deadlifts). Then i brought deadlifts back in. Then after a few more weeks i brought in pronated grip pull ups. At the time i accepted that i would always do pullups and not chinups. Well, about 6 months ago i changed back to chinups and have been doing them twice a weak pain free.
Give it a break for a bit before you do more damage. Then maybe try overhand pull ups for a while.