Here's a picture of the little guy. His name is Wheatley.
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Go back to the vet.
My vet tech wife agrees.
The antibiotics should've done the job so the cat needs attention.
I have a cat that gets a lot of respiratory stuff too. I bought her a cool humidifier and I set it up next to her favorite bed when she's really congested. It seems like it must help, because she'll mostly hang out next to it until her cold passes.
My cat is chronically congested. She has autoimmune issues but every new vet just gives her antibiotics and says it will clear up, but it always comes back.
She’s on an asthma puffer now which helps.
You might consider allergy including those from food. You can change food brands/flavors, analyse ingredient differences, and note responses. I understand vets can also prescribe anti-histamines. Good luck.