A vast majority of shelter cats or cats "on the street" (some experts dare to say about 90% of them) all have either calicivirus or herpesvirus. Herpesvirus can transpire as an "upper respiratory infection" that seems to come and go. Once they have been exposed to the virus, they have it for life, though symptoms may wax and wane or you can go years without a flare-up.

RARELY do cat allergies transpire as runny eyes/congestion. In dogs and cats, environmental allergies/food allergies/allergies in general transpire as skin related issues... ears, hot spots, chewing feet, with cats you may have hair loss/scabbing because of scratching around the ears/neck, etc. But rarely will allergies cause congestion like you're describing.

If you haven't already, PLEASE consider getting a second opinion from a different vet. There are a lot of options available to you, from minor stuff like using Viralys during flare-ups to even more major like nose biopsies.