It sounds like your cat has a common virus called feline herpes virus-1 (FHV-1). This causes upper respiratory infections, corneal ulcerations, sneezing and congestion similar to what people get when we get a "cold". because this is viral, antibiotics are not helpful. Antibiotics are only helpful if there is a secondary bacterial infection, which in your cat's case is does not sound like there is. Even so, most cats will be able to fight this off themselves with proper supportive care and some cats will have runny eyes and flareups from time to time- usually in times of stress or environmental change. In severe cases, antiviral medications can be helpful and may shorten the course or decrease the severity of the infection (the one I use most often is called Famcyclovir) but this is available by prescription only so you will need to have your cat examined by a vet in order to get a prescription. The medication itself is not usually cost prohibitive and I usually use ½-1 250mg tablet twice daily for 14 days. This can be give for longer if necessary.
While some people advocate the use of L-lysine for cats with FHV-1, a recent study did not show this to be effective in reducing the duration or number of outbreaks, so I do not feel strongly about using it. It will not hurt but it may not help and is added expense and one more thing that you have to get into the cat which may be a challenge if he or she is not eating.
As long as there is discharge, you can clean the eyes with warn water and a soft cloth. If there is nasal discharge you can use saline drops to break up the mucus and help him breathe better and you can put him in a steamy bathroom or use a nebulizer to help clear discharge as well. You can use regular saline eye irrigation (or contact lens solution) to clean around the eyes as well as this will not hurt if it gets in the eye. Since cats with upper respiratory infections cannot smell very well, you can heat up his food and offer it to them by hand to encourage him to eat. There is an antibiotic eye ointment that is available over the counter in some pet stores or feed stores called Terramycin. This can be used in the eyes 3-4 times a day to help prevent secondary bacterial infection of the conjunctiva but if he has no other signs of upper respiratory infection, you do not have to do anything as it will wax and wane on its own.
Although it sounds like an upper respiratory infection, its possible that the clinical signs you are describing have a different cause- allergies and a corneal ulcer come to mind. I recommend that testing be performed to rule out corneal ulceration (a stain of the eye to make sure there are no defects in the cornea) and if this is negative your vet can prescribe a course of eye ointment or drops with a steroid in it to reduce inflammation.
Some cats and breeds will be prone to eye discharge due to conformation and treat ducts that do not drain properly. A tear duct flush can be performed to open up these tear ducts and provide for proper drainage of the tears which are constantly being produced to lubricate the cornea. When your vet stains his eyes, he can look for the presence of stain coming from his nose, and if there that means the ducts are patent and if not, they are not patent and flushing then under anesthesia can be considered.
I hope this answers your question. If you have additional questions or want to discuss your cat's specific clinical signs in more detail please let me know.
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