Update: My followup with the surgeon went well, and now I'm free of the sling on my arm. For the next month, I've got a list of passive motions I'm meant to do with my arm (i.e., using my good arm to lift the other one). The point of all of this is getting back my range of motion. All of this while the surgical repair is still healing itself.

Still, this is a huge new thing. I have my two hands again. Huzzah. More importantly, the surgeon said I'm cool to ride a bike again, but I won't be swimming for a while yet.