Hello I am Dr. Joey. Thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 15 years of experience. I look forward to working with you.
My biggest concern based on what you reported for Joshua is the lethargy, possible fever which could go hand in hand. Unfortunately, his symptoms are vague and could reflect one of many problems. Unless sneezing and nasal discharge has persisted I am not sure we can link his signs to a primary upper respiratory infection, but if they have persisted then he may have an upper respiratory viral infection. Our older cats are certainly at greater risk for pneumonia or for this not being just an infection (bacterial, fungal, viral) problem, and instead be something like a polyp or tumor (hate to mention it but it has to be on our list at his age).
What we need to decide is if this is an emergency situation that cannot wait until your vet is open on Monday or if he is stable. If he is profoundly lethargic (antisocial, not moving, perhaps worsening with this) and not eating/drinking and/or has any vomiting/diarrhea or difficulty breathing, then this is an emergency and you need to have him seen today. This really cannot wait.
If he is eating/drinking and has no emergency signs, then you should try to tempt him to eat today, especially with moist foods to keep him hydrated. Bring out all of his favorites (e.g., canned foods, tuna or other canned meat products, etc). Keep him drinking as best possible. Perhaps offer watered down broth or add low sodium broth (not stock) to his food to make it more moist. IF he is a dry only kitty then try adding broth to that.
There are, unfortunately, no "safe" medications I can recommend with his vague symptoms. Cats are very sensitive to drugs and can have a tough time processing most. Therefore, I would not feel comfortable recommending anything without him having an examination with a veterinarian.
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