I turned down the magazine that wanted to publish my story. I'm going to hold out for one of the other places that I submitted to. It's taking a risk because maybe I shouldn't be picky, but this place is pretty amateur and I'd rather get the story into a more respected place.
I feel like a jerk for even sending the story there. Oh well. At least I'm learning about how all this stuff works. I'm still happy that someone likes me and I hope that someone else out there does, too, and that this wasn't a big mistake.
Here's an article I read that really helped me figure out what to do (I also asked the advice of Brandi Wells, a much more successful writer than me):
Submitting to Lit Mags