I also had the funny wheezy cough intermittently not associated with illness more mechanical irritation. My guess is that it is related to the thyroid
I learned recently the benefit of having the TPO antibodies tested. GP ordered this test from their office blood draw after my request and it took a couple of days to show levels 800+ ...normal is less than 30. From the knowledge I've gathered here on this site that shows Hashimotos (auto-immune disorder?) which is chronic inflammation that the ultrasound showed on one lobe. Different issue my right lobe has a solid nodule. Lots of other more knowledgeable people just thought I share my experience, Best Wishes and DO NOT GIVE UP... doc's are people even though some look, act and sound like ducks... quack quack. It's taken me years to internalize that advice. It is not normal to be in pain and tired all the time unless you have a real Dx explaining it. STAMP IT NO ERASIES.
Would have the thyroid tested more thoroughly - perhaps TSH, Free T4 & T3 as well as TPO/Tg antibodies. The cysts are not likely to cause these symptoms.