What is wrong with my finger? I fell on my pinky finger and heard a cracking sound. It hurts to touch and move and after a couple of days it started to get swollen, and bruise. But I still have complete mobility in my finger. What is wrong with my finger?

There. There can be a sprain of a ligament, a small avulsion fracture, a fracture of the joint, a fracture in the bone in the long or oblique axis, a partial tendon avulsion, a ligament rupture. Whatmay pass for "complete" mobility may seem to be ok but a discerning exam might reveal that there is in fact limitation of motion caused but the swelling. Intraarticular swelling can impede motion or lead to subtle loss of full extension or flexion. Of course finger swelling following trauma may just be a bad bruise if the pain continues it would be worthwhile getting an x-ray as knowledge of the injury whether it is a factor or not may be a guide to return to activity with or without care. If there is a negative x-ray and pain persists it may be worthwhile to see a hand surgeon. Still be aware that a contusion or bas bruise to the finiger especially if it affect the pip joint or proximal interphalangeal joint (in the middle of the finger) can had symptoms that linger for....Months after an injury.
You. You situation is consistent with a possible chip fracture of your finger. See your doctor. You might need an xray. Best wishes.