In reply to SenzuBean:
I had this problem (or so i thought...) about this time last year. I posted a similar request and got loads of advice, the thread has been archived now but can be found here:
https://www.ukclimbing.com/forums/t.php?n=655363 - loads of useful advice and links.
BUT
I can't stress this enough. Go to a physio - preferably one who works with climbers.
I had self diagnosed this being a problem of the medial epicondyle and was managing to relieve the symptoms through some web-learned exercises, but would never have cured the problem had I not gone to a physio.
The reason being, the vast majority of self-diagnosed elbow / medial epicondyle problems end up being neurological (you've annoyed a nerve). Although your tendon will have some damage, the nerve is a contributing factor. In golfer's elbow it's normally the medial or ulnar nerve that is playing up. What causes this is different for everyone. For me it turned out that a weak & wonky scapula was the original cause, hence why just before i went to a physio i was getting pain in my neck as well as my elbow.
I'll lay out what worked for me below, but please go to a climbing physio (if you haven't already) - it will go away quicker if you do.
My routine:
1) Wrist curls: 50 reps* with a 2kg weight - rest your forearm on a bench / sofa arm and perform one set per arm with the arm fully straightened (180 degrees), at 120 degrees, at 90 degrees and at 45ish degrees (full lock position)
2) Wrist twists (a.k.a weight on a stick): 10 reps with a weight that you can complete 4 sets. With golfer's elbow the weight must always turn away from the body. Again do this with the arm at the different angles mentioned above.
-- For both of the above keep your thumb on the same side of the dumbell / stick as your other fingers, can't explain the science but it makes a difference --
3) Powerfingers Bicep curl: get some powerfingers bands, put on a band and extend your fingers fully, then do bicep curls in sets of about 15-20. The first one or two should make the sore bit of your elbow feel stiff, after that it starts to go away.
4) Nerve "flossing" exercises. This will depend on the cause of your injury, but once my physio found the exercise specific to me I did it whenever I had a spare moment and it cleared up the pain in my neck & elbow. Watch some ulnar and medial nerve flossing or "gliding" videos and try out some of the exercises - but you'll probably need a physio to find the right one.
*Any physio's or medical people out there please correct me if i've misunderstood or used appalling layman's terms. I was advised to keep a high rep rate for this exercise as once a tendon is damaged, the body sends collagen to fix it, when it needs a lot this can be "bad collagen" that will not fix the tendon in the way we're hoping. If you don't use the tendon the collagen will sit there until we use it again and cause the same problem to occur. Doing multiple wrist curls without too much stress (weight) allows the tendon to re-learn the action we want it to perform and allows "good collagen" to go there, thus getting the result we want. I mention this as i've seen conflicting advice on whether to use a high / low rep rate & weight combo.