Had tennis elbow in both arms a few years ago. Wasn’t playing tennis, but was trying to play guitar at the time - barre chords, specifically.
Never saw a doctor, but did online research, and tried all the methods already mentioned above.
None of them worked long term for me. If I started playing again, my fretting hand elbow would start hurting again - often, the same day.
What did work was this book.
Basically, it’s self treatment by deep tissue massage with a hard rubber ball.
I noticed reduced pain within a few days, and complete recovery after about a month.
I eventually figured out that the problem was caused by one of the fingers I wasn’t using to fret the chords. I was lifting it up off the fretboard with way too much tension. The muscles that flex and extend the fingers are near the elbow, and can refer pain to the elbow if they are overstressed. I never would have figured this out without the book.
These days, whenever I have pain anywhere in my body, I dig out my book, do the massage, and almost always get some immediate pain reduction.
Self treatment is not for everyone. I’ve suggested this book to at least 10 people with pain issues, and only one or two of them actually tried it. But it worked for those who did.
Note that a lot of massage therapists can do trigger point therapy, so this might be an option if you don’t want to self treat.
Also note that most doctors don’t know anything about this…at least that was the case a few years ago.