going in reverse or downshift makes a noise like metal dragging

Lately I been hear loudly every time I down shift or go reverse like some kind of metal dragging under the car. Everything shifts normal with ease since I just replaced the clutch last year, but can't figure this out? One night I did feel and hear like something ripped off and I drove over it, but I checked under the car and I dint see anything wrong.
Also in the morning when I go into first and second gear I hear a thump and feels like I ran over something