1998 Chevrolet Cavalier New Brakes not stopping

I've had my car about 4 years and the problem was rare but lately has become worse and more frequent. I've replaced all my brakesw and when \i take it to be checked they say theres nothing wrong but occasionally when \i brake my car makes a grinding sound and wont stop right away it kind of grinds to a halt after about 10 feet even thouhg my pedal is to the floor. I have almost hit other cars and gone into intersections but no one can tell me whats wrong.