Well, an example of "psychological" media that first came to mind for me would be the Silent Hill video game franchise. Rather than BLOOD AND CORPSES AND BLEAGHAGAGAGAGAGAH like in typical horror media, Silent Hill messes with your mind. No pop-out corpses, no bloodied zombies coming after you in droves. Silent Hill is the horror of being totally and utterly alone. That the games are also so heavily symbolic adds another layer of depth to them and gets you thinking about why they're even there, or what they could possibly mean. The horror is just so subtle, it messes with you until you can't think straight about what's going on around you. Actually, in SH3, you find a room at the end of the game that's filled with nothing but corpses stuffed in bags; there's so many they're literally spilling out of the walls and lying haphazardly along the ground. It's in such striking contrast to the rest of the game's subtle mindfuck that it ends up being one of the most horrifying things in the game.
Another "psychological" series would be the Liar Game manga. It's people competing for an enormous amount of money to pay off their debts, but it quickly turns into a series of gambits that would put Death Note to shame. Literally everything in the series is about deception, lying, manipulation, and why people can do the things they do. It's pretty difficult to describe, but it's definitely worth a read OH WAIT CAN'T DO THAT ANYMORE :V
But yeah seriously, if you can ever play Silent Hill or read Liar Game, do it do it do it.