M.D.
Have you determined if those things actually bother him? My reflux guy was very sensitive to my consumption of cows milk, but he was fine if I had nuts, eggs, soy, etc.
So, I ate cereal with rice milk (I don't like soy milk), oatmeal with a little brown sugar, or eggs for breakfast. For other meals I ate grilled protein (chicken, steak, salmon) and veggies. Chinese food in general was fine. I found a milk-free brand of bread and had normal sandwiches (lunchmeat but no cheese). Tacos (ground beef and salsa on a corn tortilla but no cheese or sour cream ). Chicken noodle soup (or any non-cream based soup).
Good luck. Reflux is so hard.
ETA: Oh, I missed the wheezing part. Definitely talk to your pediatrician about that. My child who had severe reflux and milk intolerance did not wheeze.