Lots of people, including me, have suffered from tennis elbow from shooting the bow. In its early stages, it is micro tears in the connective tissue in the elbow joint, brought on by hand shock. The hand shocks don't have to be violent to do the damage; it happens over time and many shots.. It is important to lay off whatever is shocking the elbow joint, in this case your bow, until it goes away, which could take a long time. While this isn't a pleasant thought, it is better than ignoring it, which could result in greater damage people mention in some of the posts above.
The first part of the treatment is avoiding the hand shocks. The second is repairing the damage. Total rest is bad; it results in atrophy of the joint. There are gentle exercises you can find on the internet which will help, ranging from reverse curls with cans of peas, to squeeze balls, to Thera band flex bars. My son in law is an orthopedic surgeon who has seen hundreds of these cases, and he says virtually all of them can be cured following the advice above. Arthritis in the joint is a different problem from tennis elbow, and while hand shock can aggravate it too, is not as easy, or maybe even possible, to cure.
Since you haven't had this problem before, the likelihood is that you can cure it easily enough over time, although of course you won't like not shooting your bow for a while. If it comes back when you start shooting your bow again, you may have to sell that bow and go back to one that doesn't cause the problem. That happened to me, and I had to sell a bow I really liked, but that was better than having to give up shooting altogether. As people have said, don't lock out your elbow when you shoot.