Can a bruise break up and cause joint pain?

Not really. I agree with dr. Carr's answer in large part. Cartilage fragments may exist, you may have sustained a bone bruise, blood in a joint is quite inflammatory, and finally your collateral ligaments could have been sprained, or partially torn.
Yes. The breakdown of blood in the bruise can cause inflammation, pain, and swelling. The joint may also have been directly injured by the accident which caused the bruise. If the bruise was not caused by an accident then medical, psychiatric, or abuse issues need to be addressed.