Out of balance tire / wheel won't be felt when braking - at least very, very unlikely on a bike.
If the brakes feel like they are pulsating when you brake ever since the tire change then either one of the rotors is bent from the tire change or there are contaminants on the friction surface (i.e. a greasy, oily hand touched the rotor surface during the change.
You don't seem to be able to describe the problem accurately (rear, squeak, front squeak, shaking ....) so diagnosis on an Internet forum isn't going to get you too far. I would suggest that you take it to the place that changed the tires and see what they say. They might be able to provide some insight as they were the last one's to work on the bike.