"Tennis elbow" is a very common pain on the bow side elbow. It is caused by microtears in the connective tissue due to the repetitive shocks of many bow shots. It will get worse if you keep doing what you're doing, whatever that may be. Depending on how far along it is, you can:
--Lay off for a week and maybe it will go away
--Take ibuprofen, which will mask the problem so you can keep shooting for a while until it gets so bad you can't shoot anymore.
--Look on the Internet for exercises you can do to strengthen the affected area.
--Get a bow that doesn't have as much hand shock, which would be a lower poundage bow and/or a bow that is designed to have less hand shock, such as a recurve with more mass.
--Learn to shoot left-handed, and shoot that way for a while.
--Shoot fewer shots every day.
Once you get it, it may never completely go away, but your choices are either to manage it and keep shooting, or ignore it until you can't shoot anymore.