In reply to JimR: I used to have medial and lateral epicondylitis (golfers and tennis) in both elbows and it hurt when I climbed. I went to see an osteopath who has cured the lateral epicondylitis and is well on the way to fixing the other one. Don't get any pain climbing anymore, just some twinges after mtbing.
Tendonitis in the elbow could be caused by any number of factors, getting a suitable diagnosis from the internet is next door to useless. For example, the problem in your elbow could be caused by tightness in your forearms, biceps, chest or back, but until your are diagnosed you won't know. (it's all of them for me!) See a professional, find out what the problem is and get it treated. If you can't afford ongoing treatment then there maybe stretches and exercises that the osteo or physio will be able to show which you can do yourself. Good luck.