Not true, topolgically the route

left nostril -> sinus -> right nostril

is another hole. So is

any nostril -> sinus -> mouth.

ears have the eardrum, so they don’t count.

For the more formal definitions of topological holes, look up Betti numbers. What we’re currently talking about is the Betti number b_1. For humans, that is at least 3 (but I’m sure I’m missing many more holes). Unless you’re missing the entire septum.