Sounds like something supporting the exhaust system might have come loose or broken. I would just move the exhaust side-to-side with your hand to see what is allowing it to move like that. There are several exhaust system "hangers" that support the exhaust system, Just find them all & you'll probably find a problem with one of them.
If you find the problem & need someone else to fix it, take it to a small local muffler shop who will likely not rip you off or overcharge you. Chain shops like Midas, Meineke, etc. often (usually?) charge 2-3X what a small independent muffler shop charges for the same work.