Is it medial or lateral? I know it’s something like golf vs tennis but people mix the two up all the time.
Strengthening exercises with a hammer seem really effective. You can look those up on climbing forums.
For the race, elbow sleeves seem ok. Same with ibuprofen.
I had this in my early 20’s when I was riding only road bikes a ton and also rock climbing a ton. It went away in time. Riding position and strength/flexibility seem to help. Time off, in my experience doesn’t help at all.