I've had two instances of pain when breathing in. One was a lung clot, and the other was pulmonary edema from either an infection or an acute pneumonitis. I have IPF-UIP, unknown, and not referred to pulmonologist for the years that my lung X-Rays came back as interstial lung disease.
There are several possibilities for the symptoms you are describing. Some involve the upper airways, such as allergy or sinus. Allergy can cause postnasal drainage, burning, and coughing. Sinus involvement can cause all the same symptoms, as well as some chest problems. It is also possible that these symptoms could be asthma. The best test for asthma is a breathing test followed by a bronchodilator and another breathing test. This measures how much the bronchodilator helps your lungs by reversing the problem. There are lots of people with asthma who have normal pulmonary function tests but show reversibility and the symptoms you describe. You might consider seeing a local Board Certified Allergist for help in making the diagnosis and getting on appropriate therapy.