I'll end this (I think).
I had a cadet in my JROTC program that wanted to serve; very much! He lost a kidney to an illness several years ago (middle school). He is the epitome of fitness, strength, agility, you name it and he has it.
He was denied accessions into the military due to DOD Instruction 6130.03, Enclosure 4, page 25: "(1) Current absence of one kidney, congenital (753.0) or acquired (V45.73) (CPT 50220-50236)."
This DOD instruction covers Medical Standards for Appointment, Enlistment, or Induction in the Military Services. He went to every "expert" physician he and his family could find; the answer was the same: this is non-waiverable.
While others above have commented on the asthma, I will quote from the same DOD Instruction; bear with me, it's fairly long, the bottom line is that based upon your description, I think your case would be disqualifying:
d. Airway hyper responsiveness including asthma (493.xx), reactive airway disease, exercise-induced bronchospasm (519.11) or asthmatic bronchitis (493.90), reliably diagnosed and symptomatic after the 13th birthday.
(1) Reliable diagnostic criteria may include any of the following elements: substantiated history of cough, wheeze, chest tightness, and/or dyspnea which persists or recurs over a prolonged period of time, generally more than 12 months.
(2) Individuals DO MEET the standard if within the past 3 years they meet ALL of the criteria in subparagraphs 11.d.(2)(a)-(d).
(a) No use of controller or rescue medications (including, but not limited to inhaled corticosteroids, leukotriene receptor antagonists, or short-acting beta agonists).
(b) No exacerbations requiring acute medical treatment.
(c) No use of oral steroids.
(d) A current normal spirometry (within the past 90 days), performed in accordance with American Thoracic Society (ATS) guidelines and as defined by current National Heart, Lung, and Blood Institute (NHLBI) standards.
I applaud your desires but I think in this instance, based upon what you've shared, that you'll fall into the same bucket as my one student.