Here is what fixed me. I dealt with this for years. Every kind of shot and meds available. Finally fixed with with exercises. The exercise is short fast and easy. Put the palm of your hand (same hand as bad elbow) flat against any surface, a wall, floor, the side of your face, roof of care while driving etc. Push the hand back over the wrist as far as you can. You will be strching the forearm muscle. The Dr says the forarm muscle has something do it with the tendons of the elbow. Do this for a few seconds as often as you can.
I tried to did it at every opportunity, at least once per hour. After about 2 weeks, the pain in the elbow began to fade, it was all gone in about 3 weeks. That was 7 yrs ago. It starts to return from time to time, and I begin doing the stretching exercises again. I know of others who have done the same thing with the same good results. Try it, it works!