Is it in the antecubital area (where the Dr takes blood from)? Do you get the pain doing any kind of hammer curl movement or wide grip rows or pulldowns?
Last year, when I was having a bit time away from the gym due to needing a small operation, I developed a pain in that region (It came on about a week after stopping the gym). I first noticed a pain when fastening my jeans buttons. The operation was actually near that elbow but was not related, I had that operation months later.
At the same time as the pain appeared I developed olecranon bursitis in that elbow (bump just appeared, didn't knock it or lean on it etc. I was getting a bit concerned as there were now three things wrong with my elbow!).
I did some reading on pains in that region and the best I could come up with was brachioradialis injury or inflamation of the bursa on the radial tuberosity (it's where a tendon touches the radius when you rotate the forearm, I think!). My pain took months to go away and I had to avoid wide grip rows and pulldowns, hammer curls were out as well.
I suspect mine was bursitis due to my olecranon bursa inflaming for no apparent reason. I think the radial one might have inflamed as well, maybe they react to local conditions?
All the best!