Just a final update:

I was able to find a medication that sometimes cures swim bladder problems. It treats for some parasites, and does not harm any fish during treatment. So, I bought some, treated the tank, and 24 hours later the sick fish is still sick and the healthy fish is still healthy.

I am taking the healthy fish out today to give to a friend for his small community tank. I'm just going to have to let the angel go in peace now, and I figure she'd like to be by herself.

I don't know why I'm so sad over this fish... Well, now that I say that I guess I do know why. My mom passed away when I was young, and I remember her keeping angels. When she died, I got some to remind me of her and now the last one of the batch is dying. I suppose it's sentimentality that's getting to me.

Thanks for the input from before, guys.