Elbow pain: bursitis?

Hi there, for a few days I have been experiencing pain in my right elbow (I am left handed): The tip is extremely sensitive to touching (even the brush of my longsleeve can induce pain) plus and push-up like movement also hurts. Further the area around the tip of the elbow is quite warm. I stopped climbing after the second day after it appeard first. I also applied voltaren gel which made it a bit better initially but actually now after a few days it seems the pain is spreading further around the elbow and sometimes I wake up in the morning in pain. At least the tip is less senitive now :( I have also tried some icing but that didn't show any effect at all (about three days, twice a day). Meanwhile now the pain has become less "stinging" but rather dull, almost as if I had hit my elbow really hard against something (which I haven't). It first occured after a bouldering session where I tried a lot of shouldery moves, most of them on crimps in overhung walls. However I had been working this problem ion the past and actually felt as strong as never before that night, so I don't think I was unrested or overtrained. Any ideas what it could be and hwo to cure it? My initial self diagnosis was elbow bursitis. But I am not so sure especially as there seems no swelling (maybe a tiny little bit but very hard to see). Thanks!