Well, if you don't have asthma then I would assume that your doctor isn't going to tell the RAF that you do infact have asthma!
I'm in a similar situation to you. I want to join as a pilot as well, though I've finished college now so I'm a few years older than you. When I was at school a teacher became concerned that I was out of breath after running long distance. My mum took me to see the doctor, he gave me an inhaler and I never used it. When I spoke with my GP not long ago, he told me that I had never actually been diagnosed as suffering from asthma.
So I assume (hope) that is what the RAF doctors will be told - that I don't have asthma.
As I said though, speak to your GP to be sure. That's what I'm going to do.