Is it necessary to purify the house if I touched a dry, impure spot with my hand and couldn't remember whether my hand was wet or dry?

Do not pay attention to your [misgivings/whispers], for turning away from them is the most beneficial cure. If you doubt the wetness of your hand when touching a dry impurity, then your hand is not defiled, nor are the things it touches, because the default state is purity until impurity is proven with certainty.