Each break is unique - you did not give specifics.
Four years ago I suffered a compound fracture to my right hand. Literally, with the hospitol gown flowing behind me...I fled the emergency service I was first offered.
Make phone calls.....ask questions!!! Get references! Talk to nurses and talk to physicians!
Your hand will probably NEVER feel right again.
I went to the surgeon the surgeons use when they injure their hands.
My hand is not "right" ... it is ugly and indented and scarred ....with an extra single key stretch in the range of movement....it aches, hurts and throbs some nights....BUT I CAN PLAY THE PIANO!!!! and that is all I requested from the surgeon.
No surgery was necessary. But the first hospitol was going to IV, sedate, and hold me on ice three days until they could bring in their expert for pinning. In time, bones will re-align themselves.
Make your own best call based on the facts....and then live with it.
Sincerely,
Gargoyle