I am sort of in the same boat you are in. I would go see an asthma specialist. I was diagnosed with exercised-induced asthma when I was 11. I recently took a spirometry test and scored above 100% lung function. If you receive a normal spirometry, show DoDMERB and they will probably pass. I feel it helps to commit your interest in being ROTC to your asthma specialist. I did and I found out he went to school on an ROTC Scholarship. He said no matter what happens, he would write any letter he needs to for me to get cleared. The face to face conversation helps. Also, you might take a Methacholine Challenge Test. You can either take it on your own or DoDMERB might request one if they give you a remedial. If you go see an asthma specialist, I would bring this up as well. If you do not know what a spirometry is, it is breathing into a tube and it measures your lung function and capacity (how much oxygen you move in and out and how much oxygen you can put in your body). The Methacholine Challenge Test is where you're given a drug called Methacholine that induces asthma (bronchoconstriction). You are increasing dosages each time. After each dose, they measure your lung function. If you get through all doses without showing a notable decrease in lung performance (20% drop), you pass. If you do not make it through all the doses or your lung function decreases more than 20%, you fail.
I wish you the best of luck! If you have any more questions, feel free to PM me!