Loud clunking noise under car rear

At night, I thought I ran over something very small (something metal), then at low speed or when idling or stopping, my car is making a very loud noise(s); clunking and banging. It appears to be coming from the rear. Recently, I was told my muffler, exhaust pipes and mountings are rusty. Could I have lost a mounting? Would explain the sound of metal bouncing behind me thinking I ran over something. I do not see anything from underneath that is dragging. Or do you suspect something more serious (costly)? I have a Toyota Solara SE 2-door coupe, 6.0 cyc. Thank you!