I would suggest having him tested for an allergy to either casein or whey, the two proteins found in cow's milk/products. While conventional/allopathic doctors aren't quick/don't want to acknowledge that these two protein allergies affect the mucous membranes, naturopathic doctors and others who work in the alternative healthcare field will tell you that they do.
I discovered three years ago that I am allergic to casein. Once I quit eating anything with cow's milk/cow milk products, my years of rhinitis/sinunitis went away, as did my bouts of bronchitis AND my asthma (as well as my chronic constipation). In fact, I actually quit taking my Advair medication in April 2010 and now, with winter here, I still have absolutely no signs of asthma. And I am on NO prescription drugs for asthma.
If you're breastfeeding, your little one is getting what you eat. You can experiment yourself. Stop eating all cow milk products as well as drinking milk (you have to be very diligent, as cow's milk is in everything--you'll have to switch to dark chocolate over 65% cacao to get away from milk--and even then, some companies still put milk in their products) and see how your little one does. If you bottlefeed, there is still whey or casein in the product. You might have to switch your son to raw goat milk, which you can get from a farmer. I would be very leery about soy--there are just too many "nos" for me to recommend it--and other alternative milk substitutes (almond, oat, hemp, rice) won't have anough fat and other items his growing body needs. Coconut milk is very good; not sure if it's recommended for very young babies, though. Your best bet is to quit eating the offending food(s) yourself, which will be the best way to help your baby. Chances are if he's allergic to casein or whey, he might also have other food allergies.
Good luck. Oh, if your Pediatrician or Allergy Specialist won't test for milk allergy (I'm going to guess they won't), I'd suggest seeing a Naturopath to have your son tested. That's how I had to get tested. It was a simple saliva test and cost me about $25-$30.