The only thing you can do on the existing walls is make them thicker or denser... that's why an extra layer of dry rock is useful... it does both things relatively cheaply.
The thing is... doing
anything to the walls is useless if the seals at the joints of the basic room shape are letting sound come around the thick wall.
There are lots of convenient things you can use to
absorb sound... which is good for managing sound that is in the room. Sound absorption materials do not necessarily help with sound "proofing"... they can absorb some of the sound getting in, but relying on absorption to control extraneous noise is the least efficient way to sound proof.
Sound absorption can help tailor the tonality of the room... that is where it is most useful... after you have settled with the sound proofing.
That's the gist of what the book I have suggested will explain.
all the best,
mike