One of my rabbits, Fable, is being treated with an antihistamine. I wrote about it here: https://binkybunny.com/forums/topic/childrens-benadryl-tx/
Based on my (abundant) experience with long-term antibiotics for URIs with my other rabbit Wick, both myself and my vet decided not to go with trying antibiotics because Fable’s symptoms are not indicative of an infection.
Considering you’re seeing yellow snot, I have doubts about it being an allergy more than with my Fable, who doesn’t really have discharge but I now know had eye congestion. While doing an antibiotic based on a culture is informative… a part of me is still bias towards a longer course or maybe even doing another culture to see if there’s something else.
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.