Since we're not there to hear your noise, it's difficult to determine exactly where your noise is being generated from.
This could be anything from a rattling heat shield, sticking brakes, a half shaft or low ATF level.
FOR EXAMPLE:
My daughter's Civic in my signature was screaching ONLY when going in reverse with the steering wheel turned in either direction, like when backing out of a parking spot.
Once I determined which side the noise was coming from(it didn't sound like brakes), but I tore into the brakes and found that the noisy side's brakes were almost completely frozen in their brackets. So, I started there.
I removed the stuck pads and cleaned the area & ground the rust out of the grooves in the hold down bracket, lubed everything including the slide pins and all is well. So, I did the exact same thing to the other side even though that side was not making noise...and found that these brakes too were quite stuck in their bracket...just a matter of time.
