(I'm not a girl, but hopefully maybe you'll like these? Warning: some contain dark themes/images)
Phantom Tales of the Night
Pet Shop of Horrors
Hajime
Three Days of Happiness
[switch] (is shonen ai, but I don't remember there being any intimate bl stuff)
From the Red Fog
Sunny (MATSUMOTO Taiyou)
(These next ones aren't labeled as psychological, but there's psychological elements. Plus the relationships are interesting.)
Totsukuni no Shoujo
To You, The Immortal
Migi & Dali
Kamonohashi Ron no Kindan Suiri
Hunter X Hunter
I want to read psychological manga. Something girl-friendly with interesting relationships. No BL&GL please.