There is an abundance of Bovine in milk, which is a growth hormone. Milk and dairy products cause a spike in insulin, which cause the liver to produce even more of this hormone, leading to more acne. Dairy also causes you to produce sebum, which leads to clogged pores, is a breeding ground for bacteria, which creates acne. In addition, dairy products can block your dead skin cells from exiting naturally, leading to clogged pores, which create acne.
Soy and almond milk are a better alternative and even though there’s no way to test for food intolerances, the best thing you could do is try different things. Try an elimination diet, where you eliminate dairy for at least 3 weeks and then reintroduce them slowly, to see how your skin reacts. That way you’ll know for sure if dairy is the center of your acne problem.