Why are my hip and shoulder bursae inflamed?

Hard to say. Usually bursa pain is associated with being deconditioned. They can also be associated with overuse and even with arthritis. Provide more info so i can help you further. Thank you!
Genetics. E.G hla-br 27 or hyperlaxity joint syndrome, or allergic reaction to current dietary content.
Overuse. It could be from a variety of reasons. Are you exercising too much or have a very physically demanding job? If you are overdoing it that could lead to bursae inflammation. If you have an inflammatory disease that could also be a problem.