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First, it would be important to find the underlying cause of the scab. No, it is not normal for a scab to last this long. If Goofy had received a bite or scratch accidentally, from one of his sisters, as they were playing, he may have developed an abscess that needs to be cleaned out by the vet and treated with antibiotics, so the problem can be resolved.
If the scab is at the end of his nose, when he bats at it, he could be causing the sneezing, as dust from his litter or just plain house dust on his paw is irritating his nose. It's also possible that he's starting an upper respiratory infection (kitty cold), and that's why he's sneezing. Conversely, if something in his environment is causing his nose to itch, he could have created this sore, which scabbed over, by frequently rubbing it. Cats can be allergic to many things in their environment, including their litter, any cleansers you're using, laundry detergent, fabric softener, food ingredients, scented candles or air fresheners (plug-in, solid, spray, any type).
Because he's batting at it, this indicates that it's bothering him, so it would be advisable to have him evaluated by his vet for a definite diagnosis and treatment, if necessary.
A skin scraping (painless) and/or fine needle aspiration (FNA), may provide more diagnostic tools for the vet. Aspirating cells from the area and then analyzing them under a microscope or sending them out to a lab for testing, will tell if there are any specific cells that require treatment.
I hope all will be well with Goofy and please let me know how he's doing and what the vet tells you. Thanks!
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