An allergy problem or lactose intolerance wouldn't happen while you were eating. It would happen after you ate it, and would have effects like a stuffy nose and the like. It also causes inflammation, but you don't notice that until you get older, so it's a hidden problem of eating dairy products. Also, cheese is cultured, and that makes it easier to handle than, say, milk. I think your problem might be a body image problem. Is it? You may be basically forcing yourself to reject food because you want to be thin. This is a common problem with girls your age. I'd think you might want to try therapy and see if you can get to the bottom of this. At your age, regular eating habits pretty much don't exist, and that's bad because you're body and brain are still developing and you need to eat what's good for you in appropriate amounts to avoid long-term problems. So get some help soon. Peace.
So, you posted this on the eating disorders forum. How is it going? Things any better? Are you wanting to eat but can't? Are you wanting to be thin? Some people are not morning eaters. I'm not, for example. I try but don't really have an appetite then. But then I have an early lunch. Are you underweight?
I'm wondering how you are doing.