Well,I took her to the vet a couple of days ago. Even before reading the answers here (thank you, by the way).

He scraped a dead layer of skin off the nose. He said he wasn't sure what was wrong. He told me that white cats were prone to skin cancer, which I hadn't known. He said the skin was irritated but otherwise looked normal. He gave me some steroid ointment to use for a week. If it's not improving by then he'll do a biopsy.

The redness is gone but now her nose looks black. I think the area is a bit smaller but I'm not sure. I took a photo today so I'd have a comparison.

I recently lost a cat to liver cancer. I hope this sweet girl isn't next. I don't know anything about skin cancer in cats. Would they have to remove her nose? She seems just fine right now. Breaks my heart..........