If hitting the brakes changes it, inspecting the brakes sounds good.
I'd do a few things. Check rotor run-out. This can create a chirp as well. I'm not sure why I didnt mention it before.
Anyhow, I just swapped the slide pins yesterday. There's a Chinese kit for 8 bucks from Autozone. I wasnt too impressed with the quality of the bushing in the kit though (my OEM bushing looked better so I left it). When you unbolt the caliper (one bolt is a 10 mm head, the other is a large, easy to strip torx bit), you can pull the bolts out. The 10 mm head one comes out by pulling it towards you (the head comes out last - counterintuitive). On the bottom boss, you can pull the bushing out of the rubber boot once the torx bolt is out. The rubber boot grips the bushing via grooves in the bushing (it's kind of a pain to reseat the bushing into the rubber because the rubber boot catches in the leading boot edge).
Anyhow, inspect all the pins and bushings and lube or replace as necessary. A sign of a hanging set of pins is that the outer pad wears more than the inner pad. Remember that the pins come with a sacrificial coating which does eventually wear off.
It should either be rotor-run out, the pins or an actual sticking piston (both pads on this side of the car will be worn more than the pads on the other side. Both pads on the bad side will be worn fairly evenly though).
This will all take a half hour or so to inspect and replace parts and button up.
Good luck.