I think it would be worth revisiting antibiotic treatment with a longer course. 10 days is very short, and having only 2-3 days of symptom relief before the end of treatment is pretty small for what many owners experience as persistent URIs.
My Wick, who was treated for a very persistent URI, had a week-in check-in for each med we tried, with the expectation that if there were improvements, we would continue it (so 7 days for the check-in, with no expectation of discontinuing soon unless the medication was clearly not working, in which case, we switched to a new med). 2 weeks is a more typical full treatment course, from my experience. When we found the right medication combo (through trial and error, 1 to 2 week courses as I mentioned), the course was started on 3/2/17 and we didn’t stop meds until 5/16/17. Sneezing was “almost gone” at 4/5/17, so you can see we continued for a good time longer. Notably, the vet did mention this did seem like a very persistent URI, abnormally so (you mentioned no symptoms 7-8 days into treatment, while Wick needed at least a month to see that, so clearly different cases!), but it gives you an idea that longer antibiotic treatment may be what’s needed. Fast forward to now, and Wick has been sneeze and discharge free since then.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.