What's a good way to check if my finger is broken, dislocated, jammed, or sprained?

A great deal: Can be learned from examination by an orthopedic or hand surgeon. It is doubtful that a patient would have the expertise to narrow the possibilities. Sometimes an x-ray is needed to help sort things out.

I : I don't think anyone can tell by the fact that you have less or more pain. A bad sprain can hurt as much as a fracture. A bruised or "jammed" joint can hurt a lot if there is a lot of swelling. An x-ray will help. Swelling deformity are exam findings but many sprains can look like a fracture and the reverse so a proper exam and the right x-rags based upon the exam will be the best way.