Asthma stopping me going to the naval academy or rotc?

when i was little i had Allergy induced asthma but it went away years ago. since it was Allergy induced and i work out regally and don't have asthma anymore i should still be able to go right? will this stop me from doing rotc or going to the naval academy please help. i even had a full physical the other day and even the doctor told me my asthma was gone.