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Hello. I'm sorry to hear about your cat.
These viral infections can take longer to resolve in our leukemia + cats. I like to use an antibiotic (usually Clavamox) along with Lysine for it's anti-viral properties. I would also recommend nebulizing him at home. You can get a pediatric nebulizer at a pharmacy. You can nebulize saline to him 2-4 times daily for a few minutes. This is the best way to moisten the nasal mucosa and help get some of that debris mobilized and excreted.
If you can't get a nebulizer, then I would just run a hot shower and let him breathe in the steam a couple times daily. You can also get little noses saline nose drops to instill into the nares. The key is to moisten the lining of the respiratory tract so that he can get the debris and infection out.
This should clear up, but it can take 7-14 days in some of these cats.
I hope this helps, let me know if you have any other questions.