Strange allergic reaction in toddler?

My 18 month old cannot eat Kraft Deluxe singles and he loves them. Every time we feed him anything with cheese, he throws up. He is not lactose intolerant because he drinks milk every day with no problems. I have been able to pinpoint this random throwing up to anything that contains cheese slices (including grilled cheese, sandwiches, cheese and crackers etc.). Am I missing something here? Is it possible that he is allergic to the way it is pasteurized or processed? Has anyone ever heard of something so strange?