This all may have been overcome by events, but here's my 2nd opinion.
One concept I learned in the military is that any bad paper must be covered by good paper.
The primary care notes that give a "Diagnosis" of asthma are bad paper. You need to have good paper, an opinion from a more expert and current source that you do not have any pulmonary diagnosis or impairment.
From what you state, I personally question the diagnosis of asthma. Wheezing is a sign of bronchospasm. Not all bronchospasm is due to asthma. Bronchitis can cause wheezing, and that was your diagnosis with your first event.
A respiratory infection can cause bronchiolitis and resultant wheezing.
I personally have asthma and am a medical professional. Although I can't give a diagnosis or treat over the internet, these two isolated episodes in the absence of other episodes triggered by excercise, exposure to cold air, and other normal triggers does not sound like asthma.
My suggestion would be to seek an opinion from a pulmonary doctor. That doctor might want to order tests such as spirometry. A Methacholine Challenge test might be performed if your symptoms and screening spirometry do not clearly or convincingly establish a diagnosis of asthma.
I found an excellent research article dealing with ROTC candidates and the issue of asthma.
Methacholine Challenge Testing in Reserve Officer Training Corps Cadets* ? CHEST
That article stated:
After Operation Desert Shield/Desert Storm, the Department of Defense Physical Standards for Enlistment, Appointment, and Induction were modified so that “asthma reliably diagnosed at any age” disqualifies the applicant for accession into the military.7 Previously, asthma before age 12 years with no subsequent symptoms or therapy was permissible for accession and entry into active duty.15 At present, individuals
can obtain a waiver to enter into active duty with a history of asthma only if methacholine challenge test results are negative.
The potential problems in applying that regulation involve concerns that inductees often cannot recall their exact symptoms, evaluation, or treatment of a condition they had as a young child.
In addition, primary-care practitioners may erroneously make the diagnosis of asthma on clinical grounds.16 Consequently, during military induction, entrance examination staff or recruiters often request spirometry testing to obtain objective evidence. If spirometry results are normal, as is often the case, a methacholine challenge test typically follows. In this setting, a positive result for the test would be interpreted as substantiation that an uncertain remote history indeed reflected asthma. Under current regulations, this would disqualify the applicant in most cases.
The good paper would be a pulmonary evaluation and negative methacholine challenge test. I hope that you get to read this and I hope this is helpful. If you do get accepted into the service, best of luck and I appreciate your willingness to serve.