Asthma diagnosis or meds (even if meds not taken) after 13 is a DQ for every SA, to the best of my knowledge, Whether it's waiverable really depends on whether the SA medical folks/DODMERB believe you still have asthma. If they do, a waiver is unlikely. If they believe the diagnosis was made "in error," you have a chance.
Sometimes you are asked to take a test that, to the best of my knowledge, essentially attempts to induce an asthma attack -- not sure the name of it. Passing it can really help. However, I'd wait until you hear from DODMERB as to what it is, where to take it, etc.
Being honest, I would make sure you are pursuing your Plan B that doesn't involve the military in parallel to your applications USAFA and/or ROTC. There are definitely cases of people in situations like your getting the waiver so there is hope. However, asthma is a tough one and, if the medical folks think you still have it, a waiver is virtually impossible.