I called the vet when he was picking at himself to ask for advice. They told me to keep an eye on him, and if he doesn't stop and makes it bleed again, to bring him in. I was told that if he stops and it doesn't bleed at all, he should be ok.

Anyway, he stopped nipping once he got rid of all the corn starch. It didn't bleed after that, either. I'm still watching him, but it seems like he'll be ok, without going to the vet. I wish he would stop scaring me like this.