A small bursa sac on the point of the elbow can become tender and inflamed from repeated pressure on the elbow. This condition, called olecranon bursitis, causes pain and swelling in the area at the tip of the elbow. It may be very difficult to put the elbow down on a surface due to the tenderness and swelling.
Arrange your desk to avoid direct pressure on your elbow. While doing work tasks, pull items toward you, keeping your elbow off the desk. If this is not possible, you may want to consider wearing an elbow pad, such as the type used in sports, on the sore area. The pad will help protect the elbow from direct pressure.