Pain in my elbow after batting practice for baseball?

I was in the batting Cages yesterday practicing my batting of course. We were just tossing the ball and were swinging normally. But sometimes if I hit the ball wrong and if I missed the ball completely my elbow would start to hurt. This isn't the first time this has happened. But it doesn't happen every single time I practice. But when it does happen it hurts for 15 sec. Now one day later my elbow is still hurts from the previous day. And normally the pain would go away an hour after practice. This time it has been 20 hours since practice and still hurts. It only hurts if I straiten the elbow at its straitest position. But sometimes opening doors can cause a LITTLE ITTLE BITTY discomfort in the elbow. I bat right and throw right and the pain is in the left elbow. I'm 16, 5-7, 140lbs. What could be wrong? Do I need to just wrap it up and rest it? Arthritis?

Thank you