Dear A.,
It sounds like your little guy has a sensitivity to milk, and I would avoid it all together. I avoid it myself, and you'll see why in my message.
My grandson is highly allergic to dairy. We discovered this when he was an infant and his mom had left him with me, along with a supplemental bottle of dairy based formula. He had a violent reaction to the formula, and I had to call her to come home from work, I was so worried.
I have been seeing an integrative M.D. who has helped me manage several chronic health problems through dietary changes. One thing I've learned is that cow's milk is not natural to the human body, and in reality, all of us should avoid dairy products (with the exception of a fresh mozzarella now and then).
I use either soy or coconut milk in place of cow's milk, and I love it. In fact, I use coconut milk almost exclusively, and soy only in my 1 - 2 cups of coffee daily.
You can buy coconut milk in the grocery store. It' similar to cream in texture. I personally like the Trader Joe's Light coconut Milk, or the ones you can get at Whole Foods. They have a nice, uniform, creamy consistency with no coconut chunks. It is not particularly sweet, and it works well in most recipes.
Avoiding dairy is part of a plan that has caused my migraines (once as many as 2 - 6 per month) and fibromyalgia symptoms to come to a virtual halt.