It’s fairly common, Gabriel.
A bursa (plural = bursae) is a part of joints that allows tendons to slide easily over bones. Uric acid crystals cause damage to all parts of your joints, and when a bursa becomes inflamed in this way, it is called bursitis. It seems to be particularly common in elbows. One member called his gouty elbow with jelly like swelling as his “jelbow”
The answer is to get uric acid under control which dissolves uric acid crystals, allowing your joints to recover.
I hope your doctor is giving you the right advice to get uric acid safe, in a way that is right for you. If that is so, please share your plan to remove excess uric acid, as a way to end your gout and bursitis. If you don’t have a good personal plan, please login and ask.