I broke a finger approx six months ago. They take bloody ages (it is not my first finger cruch as I dislocated a thumb in free fighting about 2 months before).
My rule of thumb is about 6 months for the dislocation of fingers/thumbs and about a year for broken ones before one gets full mobility etc back again.
I do loads of finger exercises/physio but this seems to be the fastest that my aged digits can heal.
You didn't say which finger and which joint on the finger. If it is the middle joint of the finger and it is still swollen I would gues you broke it. There is a tendon which attaches on the underside which, when the finger gets bent back spearates partially from the bone, lifting a little sliver of it off. I have some lovely Xrays of one of these.
I'd go visit A & E and gets it looked at. Bypass the docs and get yourself in a fracture clinic. Presume you don't have medical insurance or you could just do it privately