As always Glenn and Ethan have it right.
In a room that small, there will definitely be challenges to getting good sound, but you can do it.
Among other things, you are going to have significant low end issues.
I'd consider making
superchunks for all the corners; take your 2x4 rockwool panels, cut them in half (2x2), and then cut them in half again, diagonally. You are basically making rockwool triangles. Then, stack the corners floor-to-ceiling with those triangles. It's basically the same idea as straddling the corners with 4" of rockwool, but that extra mass of rockwool (with superchunks the airspace behind the panels is also filled) gives you a bit more low end absorption.
Ideally, you should do superchunks in ALL corners, including wall/ceiling corners.
Also, with the back wall that close to you, I'd pretty much line the entire back wall with rockwool, as well as the reflection points on the side walls and the ceiling.
In short, with a room this small you want to deaden it as much as you can. Buy as much rockwool as you can afford and get it all into your room!
Of course DIY is cheaper in terms of cash outlay, but it will require significant time and messy, unpleasant labor (rockwool irritates the skin and possibly the lungs... wear gloves, long sleeves, and maybe a breathing mask) on your part.
If you don't want to go this route, Glenn and Ethan can hook you up with some killer prefab solutions.
Good luck!