If the common wall between you is "drywall’ on your side (we call it "Gyprock Sheet" in Australia).What’s the best way to soundproof a room on budget
I’m starting to research ways to reduce sound transmission through a wall
You should remove it your side, put compressed "pink batts" (insulation) in the cavity all over, and then new "Dry Wall" nailed back over it to compress the pink batts in the cavity and paint the new wall. I held the batts in place with string thumb tacked into the wood battens while the new drywall sheets were nailed up.
Cost
"dry wall cheap as **** so are pink batts, and you don’t see anything, looks like it did.
Cheers George