If someone has great oral hygiene but there is a foul smell coming from their nose and mouth, what could that be from and how would you get rid of it?

Sinuses: Sinuses may give you symptoms like that. Chronic inflammation and not necessarily infection may trigger foul odors. Check with your doctor please.

May have sinusitis: Bad smells sensed in the nose are usually from a sinus infection. A doctor can look inside the nose to see what is up there, and then prescribe antibiotics as needed. Kids sometimes put a bead, a piece of foam, a button, or other little object up the nostril (the object has to be removed).