I had a appointment with the physical therapist just now (about my hand, of course).
As I'd suspected, it's completely fine--I didn't lose any of my range of motion (at least compared to my other hand, since no one measures their normal range of motion just in case they hurt themselves!), and I just need to strengthen it a bit.
So she gave me some silly putty.
I mean, special physical therapy putty, which comes in different densities, so you can build up to a harder putty as you get stronger. I'm supposed to spend a few minutes a couple of times a day squeezing it as hard as I can, making sure I work my fingers in as far as they'll go.