Have you taken your cat in a pet carrier recently? Just wondering because we had to put our cat Stinky in a cage a few weeks ago and she didn't want to be in there and pushed her face against the metal cage door over and over and this was the result. Next time we are going to pad the door with something! Or buy a soft carrier.

Also, she is dealing with a food allergy and has to eat Hills D/D Venison and Green Pea and does pretty well on it but she has an upper respiratory virus that comes out at times of stress (being stuffed into a cage qualifies) so I had to give her Lysine for about a week mixed in wet food and unfortunately that set off her allergies so she's been overgrooming herself and very itchy. That too can cause her nose to look like this but this time it's quite noticable because of her time in the carrier.
So I was also wondering if your cat is grooming more than usual or chewing at herself? This 'could' be the reason and might be a food allergy or environmental allergy of some kind. Just wanted to mention it. Below is a photo of Stinky with her nose a bit beat up.
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