You won't like this advice, but I would shut it down and get it checked out. One part of developing as a player is learning to listen to your body. If you take a few days off and it still hurts, the best thing to do would be to see a doctor who works with athletes.
Once your arm is better you may want to have someone take a good look at your mechanics. If your elbow is hurting you may be doing something wrong. My son is a catcher and he used to throw too much with his arm, using his elbow. Sometimes his elbow hurt, and eventually he irritated his biceps tendon. Improved mechanics, lots of time in the weight room, and better arm conditioning have helped him immensely.
Good luck.