Well, I still have not seen a doctor. I gave it a few days to see how it would go. At this point the finger is still bent. However, there is less pain and I can use the finger, but still have to be careful with it. If I try to force my finger straight I can feel tightness in the finger, like the muscle or tendon is won't allow me to fully extend it. And if I hold my finger right below the joint and try to wiggle it it feels like the bones are grinding. I believe the injury is called mallet finger (which someone already mentioned). I will probably go to the doctor in a few days. I was reading that a deformity can develop if it is not corrected the right way.