So I would need to see your assets and scene structure to be sure, but is the problem just the orientation of the sprite? If you sprite is 90 degrees off, then that would be the source of your problem. look_at should align the sprite to the positive horizontal axis.
In other words, if you replace the godot head with an arrow that points from left to right, is it still 90 degrees off?
Also, if you don't make some rules for deadzones etc, you are going to have some real trouble.