My cat has a red bloody sore on her nose, what is it?

I have a cat, she is about 12 years old. I noticed a couple days ago that she had a small bloody sore on her nose right in the very center of the part that separates the nostrils. I thought she just rubbed it on something and that maybe it would go away. Well, today I noticed that it is getting bigger. About three times the size it was. It is dark dark red, no puss and no head, like a zit or anything. Just a dark dark red scrape sort of. There is no swelling, in fact, it looks like some flesh has been scarped off. She hasn’t been licking it or scratching it and is an indoor cat. We have another cat, but they stay away from each other. What do you think it is?! HELP PLEASE!?