It sound like arthritis, but I would try hot water on it or a hot pad.. Capsaicin cream could help as well. If all else fell get a second opinion.
Both of those are unlikely as I have full range of motion with the finger and no pain in normal function. It also doesn't hurt when I press or rub the affected area. It only hurts when I pull the finger across the rest of the fingers (either in front or behind) laterally. Or if I make a tight fist.
Could you have dislocated your finger, or perhaps you have a bad bone bruise.
Hope it heals soon
D