I am in a similar situation to yours; I had asthma when I was younger, but I'm fine now. DoDMERB is very black and white and they will DQ you if you have any diagnosis of Asthma after your 13th birthday in your medical records.
Here is how it went in my case:
I got my medical tests done and DoDMERB requested my medical records from present to birth (standard protocal if there is some history of asthma.) After sending in 2lbs of information I received a DQ because I had been prescribed a asthma medication after my 13th birthday (even though I hadn't used my medication since the age of 12.) I have just recently gone to the doctor to have him send a letter to help my chances of getting a waiver.
If you have further DoDMERB questions, I suggest you post them over on www,serviceacademyforums.com (there is a retired DoDMERB examiner there.)
Best of Luck