Hi Susan Mary, welcome to pets.ca. Sorry that you and Max are having a rough go of it. I hope you're able to get him an earlier appointment, breathing problems can be very serious. Expanding on Growler's suggestion, I think it would be a good idea to get a chest x-ray or ultrasound if you can. Heart disease and diabetes go hand in hand, so it's important to rule that out before assuming it's related to allergies.
As for Max's diabetes, have you ever considered testing his blood glucose levels yourself, at home? You can use a human glucometer and lancet device, and it's waaaaay cheaper than having to take him to the vet so frequently. Plus, there's nothing like being able to know instantly what his glucose level is. It would give you much more info on how well his diabetes is regulated overall.
As for food, there are much better products than Iams. Not sure which variety you're feeding, but Iams tends to be heavy on the grains, which translates into sugary carbs, not good for a diabetic as you know. A grain-free, higher protein and lower carb food along the lines of Orijen or Wellness or
Nature's Variety is preferable. Even better would be a raw diet. But be cautious with a diet change until you're testing Max's bg yourself, as his insulin needs may drop. I'll try to find some links for you on home-testing so you can decide if this is something you want to do.