Pesach is the time for burns - everyone out there kashering things, be VERY careful. And use a flashlight for bedikat chometz, not a candle.
So. She said I did the right things (thank you, aunt_becca). She prescribed me an antiburn ointment which two large pharmacies, one of which has the most esoteric drugs, did not have. So I went to a local one because even though they wouldn't have it, either (and they did last month and didn't reorder), it would be a lot easier for me to pick up tomorrow. That and keeping it covered.
My current solution? roadnotes's idea. I'm using a 4" wide ace bandage. This will be over two gauze pads - one nonstick over the raw spot and one regular over it. I can shower so long as I put ointment on right afterwards. As I will not have the burn ointment in the morning, I'll use antibiotic ointment then. I'll put tape over the hooks to keep them in place.