Need advice on diet/allergies/snout, questions

We have a new bully mix. He is 3 yrs old and vet said he is healthy, but vet also said he has a short bulldog pallet, causing reverse sneezes he needs help with sometimes, lots of snorts and coughs, and just seems like he struggles a bit.

I know these breeds can tend to have allergies, Am wondering if there’s anything else besides “no chicken” that might be able to keep inflammation down, or any supplements, any knowledge you all want to share? Maybe humidifier at night?

He doesn’t have skin issues yet, just dry. We started giving him a sardine a week per vet. We are also going to look for a new vet soon (long story) and ask them the same questions, but until then, is there anything else diet wise I should know? I’ve only had pits before, and they have longer snouts with less breathing issues.