I have food-triggered acne, but I've found it to be triggered by grains, nuts, and fruits in my own case. However, if I were you I'd try SCD-legal raw cheeses. My guess is that you'll find that the harder and longer aged the better.
Sucks, doesn't it? I can't eat cow's dairy, either, or I break out in huge cysts all over my face. I find that all forms of goat dairy are easy on my skin and have been eating it consistently for over a year now without an acne flare-up. (I noted the duration because it usually takes up to two weeks for the cysts to develop after I consume cow's dairy products, but I realize everyone is different.) Goat yoghurt and goat cheese are also safe for my sensitive tummy, too. :)