I would just buy another set of pads for the front from autozone or something. I had an issue with a constant squeaking(more like a whirring) sound while NOT braking. A different brand of pads solved the issue....and they were only like 30 bucks or something.

Also try anti-squeal paste for the pads...not the cheap spray can stuff but the latex/glue like anti-squeal compound. Again...something that worked for me when I had my doubts.

I would think this would cause a constant sound even when not braking.