You do not say where around the elbow you are having pain.
If it is on the posterior aspect, the point of the elbow, then it could be olecranon bursitis or triceps tendonitis.
If it is over the inside (medial) or outside (lateral) aspects, then it could be epicondylitis. The lateral epicondylitis is sometimes called tennis elbow. On the medial side, it is called Little Leaguer's or golf elbow.
If it is really bothering you, you might want to have your physician take a look at your elbow. Good luck.