I'm going through something very similar right now. About 6 months ago, it started with a super stuffy nose and difficulty breathing in through my mouth. Several specialists later (ENT, Pulminary, Allergist, etc.) and no one could figure what was wrong. I did not have asthma. I did have a terrible sinus infection, but even after that was resolved, I still had the stuffiness and lung issue. I also had a series of allergy testing done and discovered I have no allergies.
Frightened and unsure what to do next, I decided to see an integrative medical doctor (M.D. who also practices homeopathic medicine). After pushing around on my stomach it was discovered that my digestive system was bloated and very painful (I knew my stomach was bloated but didn't experience any pain until he started pushing on it... something I wouldn't normally do).
He suspected a bacterial infection so I had a simple blood test done. It was confirmed... I have a H. pylori bacteria that took up residency in my stomach.
The way it was explained to me is that this bacteria has been linked to one of the main causes of ulcers, stomach cancer, and stomach inflammation. Your system goes on the defensive creating more stomach acid and histamine. Because of this, your body can become ultra sensitive causing allergic reactions when you had none before (i.e., food, sinusitis, etc.). Also, the increase in stomach acid can cause issues with your esophagus and lungs just like GERD.
I am working closely with my doctor to erradicate this bacteria taking several courses of antibiotics (yuck), high dose of probiotics (taken 2-3 hours after the antibiotics), proteolytic digestive enzymes with each meal and as well as fiber. I did notice that increasing my fiber (slowly) helped with the nasal stuffiness, though if I am unable to "eliminate" regularly, my nasal stuffiness comes back (I have slow digestion, too - I had my gallbladder out about 6 years ago). One thing that helps me is an Osmotic laxative that I do about every 10-14 days. This laxative is non-habiting forming.
I may still have to see a gastroenterologist. Hope this helps.