Polojesse, you mentioned that you have been to see a doctor to have blood work performed - but have you been to an endocrinologist yet? If not, go!
I am the poster child for pneumonia, colds, bronchitis, sinus infections and allergies. Everytime I would go to see my gp, he would prescribe enough antibiotics to kill a horse.
It wasn't until I started researching online after being diagnosed with hashimoto's did I read that individuals with low thyroid function "do" have more respiratory infections than others.
In my case, having the hashimoto's/auto-immune disease, my body doesn't know good cells from bad, or which ones to fight off.
So, i'd go see an endo and mention that you also are a poster child - of course with any other symptons you might have.
Reallady