Lake Tahoe, CA
Several things could be going on.
Cats’ noses are prone to trauma. Cats that go outside may get into fights with other cats and suffer scratches on the nose. Indoor cats can rub their noses raw on windows or walls as they try to seek exit from a room or building. Caged or crated cats often become agitated and injure their noses looking for a way out.
The end of a cat’s nose also is a common site for the development of cancerous and precancerous lesions. White cats are at greatest risk. Sun exposure is not required, but it increases the risk. The most common type of cancer to develop on cats’ noses is called squamous cell carcinoma.
Cats do not suffer from immune-mediated skin problems on the nose as often as dogs. However, these sorts of problems do occasionally cause issues in feline companions.
Finally, certain bacterial or fungal infections can lead to redness or ulceration of the nose in cats.
Any non-healing sore on an animal should be evaluated by a veterinarian.