When dealing with squeaking brakes, you might find that your brake pedal is also spongy. This condition is caused by air in the brake lines. Air can get in the brake lines when someone tries to bleed the lines without using the proper technique. When this happens, it can allow extra air into the lines and this can lead to the spongy feeling.
To fix the problem, have a professional bleed the brake lines with the proper type of sequence for your make and model. At that point, the brakes should feel like normal again.