I'm a bit puzzled by this. I take it that the restart allowed you to get into the Password and Security settings then you say none of your passwords worked. What were you trying to do?
Everything on that "page" of the phone is password secure. When I tapped Password and Security, I was asked for a password. I just went back to that "page" and tapped "iPhone SE," and it requests answers to two security questions. Apparently, Apple is protecting me from myself.