What makes my front wheels squeak while driving?

If the steering is not shaking the imbalance must be in the rear. You need to have the wheels properly balanced as well as make sure all the mounting surfaces are clean and smooth. This means no corrosion build up on the hub face,rotor, and rim mount area. This can cause glazing on part of the rotor resulting in squeaking. Many shop neglect to properly clean these surfaces during brake replacement. Also make sure rims are hub centric or have spacer rings installed if you have aftermarket rims. The lug bolts need to be torqued correctly and have the correct taper or the wheels can come loose.