"Shearing" was added for up-down look in Heretic, for the non-Doom engine descendants Duke Nukem 3D and Rise of The Triad supported it as well. I don't remember if it could be bound to mouse movement in any of these games.

They were bound to keys for the DOS versions from memory. Forget when the mouse look was supported but the view was highly distorted so mostly useless until later ports enabled proper 3d rendering.