Dairy gives me cystic acne, constipation, and diarrhea. is this an allergy or intolerance?

Intolerance: It sounds like lactose intolerance is likely causing your symptoms of constipation and diarrhea. Avoiding dairy (although you might try Lactaid products) should help. It is likely the inflammatory activity association with bacteria and clogged pores that is contributing to the cystic acne. One theory is the hormones in dairy products might contribute to oil gland production. Good wishes:)

Intolerance: These are not signs of allergy. An allergy would have systemic signs like rash, itchy, hives etc. This may be a lactose intolerance. The acne may just be a coincidence