Is it true that sleeping on my sides increases the folds on that side of the face?

Probably not true. A normal person should not get increased lines or skin folds on his face due to sleeping on his side. Many people sleep on a favorite side, but we rarely see people with one side of the face much more wrinkly or folded than the other side. Many people (unfortunately) sit on their butts all day long at work, but we rarely see wrinkly, folded butt cheeks in working-age americans.