Small mobile tender mass when leaning on elbow. is it a cyst causes my elbow pain and how do i fix it?

Cyst on elbow: It seems you have a cyst and only way to get rid of it is surgical excision.

Olecranon bursitis: The olcranon process is the back of the hunge joint at the elbow. A bursa is a sac that sits over the outside of a joint to cushion the soft tissues from injury. The olecranon bursa can become inflamed, usually from trauma, like leaning a lot on your elbows. An inflamed bursa is called a bursitis. It is often treated with anti-inflammatoies, ace wraps, aspiration of fluid, or a cortisone injection.