Before suggesting something as drastic and last resort as cortisone injections, your doc should probably try to work out which one (tennis/golfers) it is! Lateral epicondylitis (tennis) or medial epicondylitis (golfers) – the usual difference is the type of loading that triggers the pain, and where the pain is (normally inside vs outside of elbow).
It might feel like you’ve had it a long time, but it’s still possible that with the right combination of rest, stretching, massage and exercise, it may resolve itself.
I’d recommend a good sports physio as a first stop. If you can find one with some experience of climbing injuries, then he/she may be more familiar with the condition.
I had tennis elbow for about a year, and managed to clear it up with physio, stretching and exercise. Perversely, resting can actually make it worse in some instances.