The tip of my finger won't move?

Mallet finger: If you have had an injury it sounds like you may have ruptured one of your tendons of your finger. See your doctor for a splint and further treatment

Well: Really Need more information. Did you injure the finger? Best to see your doctor for exam

Usually: this would be due to trauma or arthritis. Either there is swelling with fluid compressing the joint or bony changes that compromise function of this small DIP (distal interphalangeal joint). It would be unusual for you to have an isolated nerve or vascular dysfunction that only involved the tip of a finger. Apply heat, massage it..if it doesn't improve, an in-person eval with a Doctor is in needed

Fingertip: Loss of motion can be due to attending injury can be Arthritic joint or can be due to an injury. If you've had a recent or you need to get some x-rays you need to see someone to assess your tendon. Some people are born without joints in there distal fingertips but if that's not the case another reason is arthritis