Ya sure you're not running a mod which alters mouse/movement behavior? I've been playing on PC since day 1, and in 3rd person mode the mouse *always* dictates movement direction, as long as I'm moving and also not using the "animcam" console command or something.
As Remos said... you *have* to be running a mod in order to make the character pull a 180 and face the camera while moving in reverse. I know of mods which will induce such behavior, but the vanilla game will *not* behave this way. Ever.
Edit: Maybe you installed an animation mod, didn't like it, then got rid of it but it didn't 100% uninstall for whatever reason. Look to your ..\steamapps\common\skyrim\data\meshes\actors\character\animations\ folder. If it even exists. If it does, and has a bunch of .hkx files in its subdirectories, then there's your problem. Or at least part of it.