You pose a good question about "bursitis" with your elbow, and I think that I can give you some good information, and point you in the right direction. First of all a "bursa" is a thin slippery sac that acts as a cushion and decreases tension between bone and soft tissue in different locations of your body. In your elbow there is something called the olecranon bursa. The olecranon is the pointy part of your ulna that forms the tip of the elbow. Olecranon bursitis (the "itis" meaning inflammation) usually manifests itself as a swollen tip of the elbow that protrudes out and is tender. It can be from trauma, or can develop over a long period of time from pressure (like sitting with your elbows on a hard table for weeks to months). This could potentially be whats going on, but I can't see your elbow to tell you if that is what it looks like. You mention playing softball, so I also think that it is possible that you have developed a tendonitis in your elbow which can give the symptoms you describe. I would recommend making an appointment with an orthopedic doctor
to get your elbow looked at. They will be able to give you a better idea of exactly what is going on once they examine your elbow. Best of luck.