"Food Allergy" ...Look, go back to square one. Before the "heat issues" before any problems. What was he eating? What, if anything, has changed, including food that might have been given to him at the daycare?
If he was on other food and there were no problems...well, begs the question. Why change?
I have a friend that has just changed her Dogo to raw from Nutro...dog is sick. Retrace your steps...where was the dog healthy...what was he eating. You have 2.5 years of experience...where was he the healthiest. Recreate that. As for environmental...well, yeah, they are affected by indoor allergens, just like us. Filters...benadryl...vacuuming...cleaning their personal spaces. Regular baths/every six months. And removing from their indoor/outdoor environment any toxic plants; however, plants are probably your least problem.
My Cane Corso has mucus coming out of her eyes...why? She is a Mastiff and, basically, it is natural for them. When her nose waters a lot...yeah, she had a cold...it stops after a few days, (just like a human.)
I think you are probably fine. We all over fixate on the burps and farts of our dog's lives. We are "Uber" moms and dads. Our pups mean the world to us..., but we need to take a page out of the mom with five kids handbook, "if he isn't bleeding, he's fine." Just keep an eye on it, but know most of these things are transitory and tomorrow he will likely be as right as rain.
(Of course, honestly, I will still worry myself sick over every burp and fart....
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