ok first, soundproofing will require you to add mass to the existing wall for modest reduction or drywall removal and a decoupled system installed for maximum reduction.
As for the echo in the room, as you can see already by removing the carpet you have increased the problem so you would have to put in a fair amount of soft surface or absorption panels to reduce the echo of the room.
How would you like to proceed?
Randy S.
760-752-3030
randy@soundproofing.org