I believe you because I have been on a dairy-free diet for a few weeks and my skin has greatly improved. It has been proven that refined sugars and milk cause acne. Milk still has natural cow hormones in it, even if it is advertised as hormone-free. Eating refined sugars will cause a spike in blood sugar, and as a result androgenic hormones are released- leading to break outs. I either drink almond or coconut milk, and I use organic agave if I want to sweeten something. Agave is low glycemic so it doesn't raise blood sugar. Reducing gluten in your diet may help too.
For dairy/gluten free recipes go there: elanaspantry.com
She has many great recipes and i use them all the time