If you do in fact have asthma it will be very difficult. Even if you don't but were disqualified for asthma, it still could be difficult. Medical records from my childhood said I had asthma but that was never determined by a test, just a doctor's word. I was disqualified in November, denied my waiver in February, took a Methacholine Challenge Test and wrote a rebuttal letter to prove I didn't have asthma and was just cleared up in early April.
If you can prove you're fit and are determined to get in, you should be able to make it happen.