Hello and thank you for your question.
Although I'm not an ENT (I am a dentist
) I thought I would throw my two cents in. What I have seen in my practice is that patients that still have their tonsils develop tonsiliths within the grooves and invaginations of their tonsils. These tonsiliths are hard calcifications of minerals and bacteria. They cause a nasty odor that when breathing you can actually smell. When you said you swallowed something hard, it may have actually came from the tonsil rather than the nasal passage.
The facial pain
sounds like a sinus
related issue. If you are unhappy with your doctor you have the ability to get a second opinion
to see if another ENT decides it may be something else worth looking into.
Best wishes and good health