Clicking while braking at low speeds, felt through pedal

I have a 1998 Cavalier coup, 115,000 miles. When I brake at slow speeds (usually in 2nd gear or lower) I feel and hear a clicking sound in the brakes, almost like something is spinning or getting caught. I've also noticed that when this happens at night my headlights flicker slightly. I've had the brakes completely replaced about 5,000 miles ago (admittedly long overdue); the mechanic (granted, it was at Monro Muffler) didn't see anything. I'd love to hold on to this car for as long as possible, but this noise makes me very nervous. Any insight is much appreciated! :D