Army and Asthma, is it 'likely' to be allowed in the army as a recruit?

I was medically diagnosed with asthma after being born two weeks early. I don't know what asthma feels like because the last time I 'supposedly' had an attack I was to young to remember. So being as it I haven't had an attack in over 13 years, plus the fact that I was given unecessary albuterol up until I was 14 years old, will this require a waiver from meps to be able to join. I would really like to join. It has been a dream of mine for a long time, and the recruiter did the hole, 'come into this secluded room thing, and heres whats going to happen, and heres what you should do', regards I am not ok with what was derived from that little secluded chat. I have done xc, track, all those sports, and I have had no problems breathing, and I doubt I even have it. Will this be a problem when I decide to make the trip down to meps?