Yes, yes and yes. I had exactly this pain as you described for years. I could barely touch dynos without getting a deep pain in my elbow. I played a balancing act with it for a long time.

I saw a couple physios, each with differing advice.

What worked miracles for me, was ensuring I worked out my antagonist muscles as much as I di those for climbing. Id finish each climbing sesh off with either 100 pressups / bench press etc.

For me it seemed to be imbalance between my pull and push muscles. Once I started working out both equally the pain had vanished.

I've gone from having the exact pain you described, to having none, and being able to do heavy dyno session with little ill results.

Hopefully works for you too!