So, I took the bike to a local mechanic. He said he took the brakes apart completely, and nothing was damaged. So he cleaned them up and put them back together. He explained to me that the wheel was rolling more freely now, but because my pads are nearly worn to the wear bars (which I already knew and was planning to replace them next spring), the brakes are still binding a little because the farther the pistons comes out, the hard it is for them to retract perfectly straight, causing the little bit of binding. But it's nothing to worry about, he said, it just needs new pads.
That information cost me $91 (2 hours of labor plus brake fluid).
When I got home, I put the bike on its stands, and binding is exactly the same as it was. I'm hoping he's right and that new pads are all I need.