Car shakes when I press brakes

Yep-- probably a warped disc rotor. Usually the cause is from overheating the brakes, especially if they get wet when they’re really hot. I’ve never heard the overtorqued nuts cause, but I suppose it is possible. Cheaper rotors are also much more prone to warping.

They may be able to put the rotors on a brake lathe and shave off the high points, but depending on the make and model it’s often a cheaper just to replace them.