The quickest remedy is to slightly bend your elbow. If you let your arm hang, just stand up straight and let your arm relax it will be bent ever so slightly. This is the amount of bend needed. But that is not a long run strategy, because you won't be able to shoot well with your bow elbow bent.

The true fix to this is to train your muscles so that when you extend your bow arm it doesn't hyper extend, I assume that is the issue here as I can't see your form. That means building up the muscles in that area. Do some bicep curls, and pushups(do not extend your arm all the way when you come up on those pushups keep it slightly bent). This is if your elbow is really super elastic, I've seen a guy who can reach over his head and wrap his hand all the way down the other side of the body to his arm pit.

The other possibility is to rotate the elbow out of the way. A simple excercise will work here, lean against a doorway with your bow arm, just like you're holding a bow. Your weight on your arm will simulate the weight of the bow. Now rotate your elbow over and over again. Do this everyday, eventually you will develop your lat muscles to automatically rotate that elbow out of the way of the string.

Another possible problem is your shoulder, make sure your bow shoulder is not hyper extended. The bones in your arm should be in line with the bones in your shoulder. Have a buddy hold an arrow across your shoulder at full draw. Your arms should be in line with that arrow. If your arm is at an angle to that arrow that means something is off with your alignment. Relax the bow shoulder and keep it down.

But it will take time to develop those muscles, to stop the pain immediately I suggest the bent elbow method and buy yourself a long arm guard. There are arm guards that go up all the way to your shoulder almost. Good luck, I hope that helps and good shooting.