My car shakes really bad while driving, more weight makes it worse.

Could be a worn inner c/v axle joint....but do not count on my guess. I reccommend you have someone exsperenced in drivetrain, suspension and steering check your car for you.

Agree with#1. Probable broken cv axle joint. Steering wheel shakes and you will usually a grinding and "marble rattling noise".

jack the front of yout car off the ground. If there is movement when jerking the wheel up and down then its a steering issue if theres movement left to right its a wheel issue