Probably medial (or lateral) epicondylitis. Medial is on inside and is also known as golfers or pitchers elbow...lateral is on outside and is known as tennis elbow.
Treatment for lateral is usually more successful than treatment for medial...in fact, I was in to see ortho surgeon last wk for mine and he declined to operate saying surgical outcome was likely poor. Gave ma a shot, which will make it feel good for 3 mos, but have and them before and they really don't do anything to solve the problem.
I have had my condition more or less for 4 yrs. Began as an occupational overuse injury and I just couldn't stay off it long enough for it to heal properly (can take up to 6 mos.). Moral of story is to LET IT FULLY HEAL or you will be on the (pretty much) permanently disabled list like me.
One thing to be aware of is that the condition arises as a result of overuse of WRIST flexion, even though it feels like it should be coming more from bicep flexion. My latest attempt to work around is to try some of those wrist straps with built in lifting hooks so I don't have to grip bar very hard (Sorry guys - have been through a full PT course of strengthening and stretching to no avail).
Fortunately I am not too much into curling and another good thing is that deadlifting does not bother me at all and can still do most Oly lifts (in my own semi-retarded, uncoordinated fashion)
Good luck, but try to give it time to heal if you can, it is a bitch to work around a chronic bad elbow for years.