Another thing you might look at is lever position, and also how you're actually holding the bars.

It's only an issue for me on the moto, not the velo, but I find if I have my fingers on the levers all the time it aggravates my tennis elbow (lateral epicondylitis, the opposite side as yours), but if I just relax and hold the grips when I'm not actively clutching or braking, I do a lot better.

On the velo, if I keep my fingers on the levers all the time I have trouble with my PIP joints hyperextending. So same thing, I try to just hold the bars and not constantly cover the brakes.