I get reoccuring sinus infections a lot, it's usually what triggers my asthma. And when those sinus infections come on, I get bad breath. I hate it, and it lingers even after I brush my teeth, use listerine, chew gum, use a mint, ect. Because it's coming from a different 'source' other than your mouth.
With that said, I used to work with a girl that had SERIOUS B.O. and horrible breath, And honestly? She was weird. She always wore gothic skirts to work, but admitted to never wearing underwear. Ever. And she was a woman. Did I mention ever? Not even... monthly... (per her admittance.) But never wore pants either, just skirts (which is fine, but in public with no undies during your monthly chick time is way over the weird-o-meter) And she always smelled like... well, you don't want to know... but it was disgusting.
So a co-worker, who was good friends with her, told her one day, "Dude, you stink. Grab a shower and save my sinuses!" LOL, she didn't care, and said that as long as she couldn't smell herself, it was all good. UGH!
My sinuses were relieved when I finally left that place.