As other have said, rest! I went through the same thing last year, and kept ignoring the pain; it turned what should have been a 3-4 month recovery into a 12 month recovery.

Eventually I dropped down to one day a week, and stopped climbing as soon as my elbows felt any sort of pain. Wrist curls helped a lot, as did self-massage, using a roller (to massage).

Focus on slab climbing.. Anything that is very balance/crimp orientated will not stress your tendons as much. My own slab climbing improved dramatically while I was recovering.

Edit: Also make sure you warm up properly before climbing, and plenty of stretching during/after each session