Two of my friends have sore elbows at the moment, while thousands of you out there in web exercise space also have them. What do you do? You can either stop climbing, and exercise altogether, and in three weeks try again. Generally the pain returns. You can try a longer lay off, which is more sensible, but might not work either.
If you don’t want to stop, try to choose routes that don’t have repetitive moves that hurt. If you still want to do exercises, that target climbing goals, switch from pull ups to hangs, or to half pull ups. If you insist on doing pull ups, vary the grip every set, and / or use gymnast’s rings that move, or Metolius rock rings which also move. There is a link between pain and the angle of the wrist and elbow. There is much less chance of pain with a so called neutral grip. A neutral grip in pull ups would be if the palms face each other. This is hard to do on most hang boards or impossible. But even a slight turn of the wrists towards each other will help.
I do lots of pull ups but I change my apparatus all the time, this seems to stop the tendon from rubbing all the time in the same place, and thus save me irritation.
Pain killers work in dulling pain, so be careful if you take them to carry on exercising as generally you only make things worse in the long run. Anti inflammation also work but again watch what you are doing as very little of the drug gets to the site of the problem. Anti inflammation plaster stickers work better in my opinion, you can try these, and it saves your liver a nasty job of filtering. One I have tried with good results is called Flector.
Good old fashion ice works also, as does hot and cold, why not try them before the drugs eh.
A last thing I have noticed is that the pain seems manageable if you switch to rowing motions. Now then there are a hell of a lot of different rowing motions to choose from, you can if you are very strong do pull ups as rows too, try some for a few weeks. One arm bent over rowing might be one of the best and most neglected of climbing exercises of all so doing them is a smart move anyway. And remember that neutral grip is less pain inducing than standard grip, so dumbbells are better than barbells. There are some bars that are less prone to hurting you, some curl bars provide a more neutral grip, try these out.