How far does the covid swab go up your nose? can it reach the olfactory nerve to the brain?

NO: The Nasopharynx is the back of your nose and throat, and has no connection with the nerves in your brain. The swab goes to the uppermost region of this area, but does not go past that into your brain as there is a fairly tough membrane that prevents anything from passing through.

Nasopharynx: Through to the nasopharynx. The olfactory nerve innervates much of the inner surface of your nose. The swab will not penetrate your skull and enter your cranium.

Not close: The test goes into the nasopharynx. Olfactory nerve fibers are much higher at the cribriform plate, and nerve itself is mainly intracranial. The swab does not contact these areas directly or indirectly.