DoDI 6130.03, April 28, 2010
Medical Standards for Appointment, Enlistment, or Induction in the Military Services
http://www.dtic.mil/whs/directives/corres/pdf/613003p.pdf
I pulled 2 sections from the standard that I think apply, (bold is mine)
c.
Current or history of recurrent acute infectious processes of the lung, including but not limited to viral pneumonia (480.x), pneumococcal pneumonia (481), bacterial pneumonia (482.xx), pneumonia due to other specified organism (483.x), pneumonia infectious disease classified elsewhere (484.x), bronchopneumonia (organism unspecified) (485), and pneumonia (organism unspecified) (486).
e. Chronic obstructive pulmonary disease (491).
(1) Current or history of bullous or generalized pulmonary emphysema (492).
(2)
Current bronchitis (490), acute or chronic
symptoms over 3 months occurring at least twice a year (491).
Read through the standard, but it looks like you should be good to go.
You should understand the medical standard, always answer truthfully, and write your response to address the standard.