Roughly speaking, tennis is the outside of the elbow, golfers is the inside. As a climber, this is an occupational hazard – currently got a flare up on the right elbow, had a nasty dose on the left a couple of years ago.
This is kinda useful in terms of the difference between tendonitis/osis, plus stretches and strengthening exercises, although not gospel.
http://www.drjuliansaunders.com/resources/feature_articles/dodgy_elbows/
In my case, physio was the answer. Deep massage, taping followed by exercise and stretching. If it’s a new injury, Perhaps icing it a couple of times a day, anti-inflammatory cream.