You could get a finger exerciser that they sell at music stores.
Like this - http://www.musiciansfriend.com/accessories/planet-waves-varigrip-hand-exerciser/580112000000000
This would help strengthen your hand/fingers as it heals.
What treatment did you have for the broken fingers? Splinting with buddy tape? Cast?
Stiffness is normal after any injury especially a fracture. If you had proper treatment I would feel comfortable telling you to exercise your hand. Squeeze a rubber ball or silly putty. Do stretches of you fingers pulling them back to just past the point of stiffness then forward.
If you didnt' have treatment and a follow up xray to confirm healing, I would get that done first. Making sure the bones aligned properly is most important.