Could well be an allergic reaction. I'd actually get that checked out, because if it is true allergies, you'd want to make sure he avoids dairy not just a home but elsewhere as well.
Meanwhile, I'd look into other calcium sources. Dietary is best and most easily absorbed (the calcium in dairy isn't absorbed as easily as that from sources like leafy greens or salmon, as it turns out), and a good calcium supplement can help you make up the difference while you make adjustments to the diet.
But it sounds worth checking out. My ears, lips, and throat/neck are places that itch when I've had something I turn out to be allergic to.