with such an accurate description of whats going on, its hard to tell where to start.
my best guess would be to check everything that touches the new exhaust you just put in. start from the block with the heat shield, which i assume is gone now, then move on to every bolt down the line. make sure they are all tightened. also make sure the little brackets holding everything on are still in place and attached to everything securely. make sure the cat is in there securely and not moving around at all. other than that i have no idea.