Why is there a bad smell after sneezing?

Some amount of stagnant nasal and sinus secretions are present in the nose and some small pockets in the nose. They become stale and start smelling. When you sneeze, these secretions are forced out of the nose and you feel the smell. If this happens very often and you also have some foul smell coming from the breath also, then one visit to an ENT specialist is warranted to rule out any nasal or sinus infection.