Do you have this lung pain all the time? I'm not sure if you have it during your period or all the time. Is it worse during your period? Have you seen your doctor? Does deep breathing or coughing make it worse?
You should consider the diagnosis of endometriosis
(EM). EM is when the tissue that lines the uterus is growing and
shedding in a place it shouldn't. It is usually in the pelvis and
causes pain prior to and often times during menses. It has been
found in areas outside the pelvis such as the lung, nose, etc. Women with these symptoms complain of pain in these areas with menses along with coughing up blood or nosebleeds.
I would see your doctor about this possibility