Is it possible to lose asthma?

Since i'm planning to join the Air Force,I need to know if I don't have asthma.I have had 1 asthma attack.It was when I was 2 and it was all due to allergies.I have used an inhaler twice.Once for a couple months,when I was like 4 (I have no idea why) and once when I was 11 or 12,due to bronchitis.I usually do get short on breath,when I run .I never really do have shortness of breath at all (except when I run like 1.5-2 miles).I do start to cough,when I over run myself and I do clear my throat allot,when I have been awake for like 20 hours.I need any help and all is appreciated.