Once I had small pebble (mebbe 1.5 mm in diameter) that got wedged near my rear brake pad. It was just barely touching the rotor. It wore itself down directionally and I never heard it while moving forward. However, when I pushed the bike backwards to park it, it would always cause a strange squeek. I was stumped and decided to tear apart the rear caliper to figure out what was going on. I pulled the caliper off and instantly saw the half ground-down pebble and figured out what was happening.
This MIGHT be your problem, based on your description, but it is a longshot. So many things could cause a uni-directional squeek.
Good luck! -Matt