Well... yes?

Fallout is irradiated particulate matter. Especially in a 1950's style (near) surface nuclear detonation, you would get a LOT of irradiated dirt and dust carried up from the blast, then spread by the rising air and irradiated by the blast. That "falls out" of the cloud and spreads through the air by wind.

The majority of fallout would be stopped a decent filter. And if you need to sit out the halflife of the most short-term dangerous stuff, a week or two would do a LOT of good.

EDIT: Pooping in the corner for two weeks is still quite a lot.