The waiver authority rests with the Service Academy (SA), in this case, USMMA -- I do not have direct knowledge of USMMA but I believe the waiver authority is the Superintendent, like it is at USMA and USNA -- if so, that person is advised by a medical team. (At USAFA, unlike the other SAs, the waiver authority is the Flight Surgeon, not the Superintendent so once the docs decide "no" you have no appeal.)
My DS had the same reaction as you did (hives) to pistachios when he was 6. USAFA required him to do an allergist supervised "nut challenge" to prove he was no longer sensitive. A "nut challenge" is where you are fed increasing amounts of the nut over a prescribed period of time in the doctor's office. It seemed like he had to eat well over a cup of the nuts for the total test. Unfortunately, he developed hives just prior to the last dosage of the nuts. Based on the hives, USAFA denied his medical waiver, but Army ROTC granted him the medical waiver after he was selected for the 4 year Army ROTC National Scholarship.
You can use the search tool in the upper right on this forum to get other stories. Just plug in "nut allergy" and you should get several threads. From my reading and our experience, it appears USAFA and AFROTC are the most "conservative" with this allergy -- I have found no cases where a nut allergy has been granted by the Air Force -- and the Army (West Point and Army ROTC) seems to be the most "reasonable" with this condition. The Army seems to be willing to grant the waiver for tree nuts provided reactions aren't too bad. (Getting a waiver from anyone for Peanuts is another story.) Navy, Coast Guard and USMMA seem to be somewhere in between AF and Army, but I do not have direct experience with them like our family does with Air Force and the Army.
It may be USMMA won't really review your waiver package unless they decide they want you because you are a very competitive candidate. That is how USAFA and USMA opperate.
Best wishes to you.