I've broken a finger before. Technically, it was just a hairline fracture, but I thought it was only sprained so I didn't get it treated and had the same type of ROM problems.
What really worked for me was this: fill a glass with hot water and soak the finger in it while you watch tv or whatever. Just bend and unbend the finger repeatedly while soaking.
It took a few weeks to get back to normal, which sucked since I couldn't really do my normal workout, or make a fist for MA training. Good luck with that.