From what I've read tennis elbow is an over use issue.
But I'm wondering if (referring to the string elbow)there is a common mistake people may make when drawing the string or on the release that may promote a tennis elbow situation in the string elbow.
Tension in the back of the hand and forearm from drawing with the arm muscles could cause tendonitus . Try a deep hook, relaxed hand and arm, drawing with the back muscles. Search for Arne Moe's (Moebow) videos on rotational draw here and on Youtube. One of, if not the, biggest improvement I've ever made to my shooting.
I've never had tennis elbow in my string elbow, but I have had it in my bow elbow. I think a major cause of it on the bow side is hand shock. The cumulative effect of small shocks from shooting many, many shots eventually can result in inflamed tendons. When I got it, it took quite a while to get rid of. You don't want to completely lay off doing things, because that can result in atrophy. You don't want to force yourself to keep on shooting the way you were either, or mask the symptoms with too much ibuprofen. So it's kind of a delicate balancing act to work your way through it. In addition to cutting back on my shooting for way longer than I wanted to, and switching to a bow with less hand shock, I found some exercises that were useful, such as the Thera Band Flex Bar (see Amazon), and some other exercises I picked up by doing an internet search on tennis elbow.
I've been free of it for several years now, and can comfortably shoot up to a hundred shots every other day or so without any pain. The other way it's a balancing act is that while it probably is an overuse issue, once you build yourself up to where you can shoot a lot of arrows without pain, it sort of helps to keep shooting a lot of arrows. I think it helps not to make any major changes, like dramatically increasing bow weight or switching to a bow with more hand shock.
Although I am NOT a doctor or a sports trainer, I am firmly convinced that many drawing side elbow problems are a result of tension in the upper/lower arm that strains the tendons in and through the elbow. Using the angular/rotational draw, IMO, makes that elbow just a free moving hinge that moves because the bones are being moved by back and rear shoulder muscles. So the elbow joint just moves freely with NO tension in the tendons.
No or even less tension, will reduce "tennis elbow."
Arne
Believe it or not I got it bad years ago from lifting my heavy briefcase in and out of the back seat to the front seat of my car. I was a salesman and it was an occupational hazard. You can get it swinging a hammer, lifting a heavy tool bucket, swinging a golf club or tennis racket.
I had tried the rotational draw, it just didn't feel as comfortable as a straight draw. However it took more focus I thought to concentrate on keeping the back muscles working with a straight draw than it did with the rotational draw. When I get back to shooting I'll start practicing the rotational draw more. At first I didn't like the deep hook, now I wouldn't have it any other way. So I probably just need to work with the rotational draw longer.
I ended up with tennis elbow on my bow arm last year, took a long time to get rid of. Believe it or not, I found the cause to be from pulling arrows from a dense foam target. The target did not give up arrows easy and I often pulled them out while standing to the side of the target, causing stress to my tendons. Just food for thought.
It's due to tension in the wrist, first off, lay off all pulling of any kind. Second use Ice wraps, then work in wrist stretches, and then wrist exercises. When you start to feel better and return to shooting keep you wrist straight and use less hand tension when gripping the bow.