I took my car to a mechanic and he replaced rotors and pads and my car still shakes when I apply my brakes.
It's not unheard of for some mechanics to charge for repairs that were incomplete or even never done. You'll need to judge how trustworthy the mechanic you used is.
You state that the rotors were replaced, but are you sure that's what was done? It could be the existing rotors were resurfaced. It could also be that the rotors were replaced with used ones which were also warped, or even that they were not worked on at all.
Assuming new rotors were installed, if you still have the same problem, then it could be an out-of-balance tire, a warped rim, a bent axle, or a suspension problem. Braking causes changes to the stresses the suspension handles, so it can definitely make a problem become more noticeable, but there is normally some evidence of the problem even when not braking.