We sound proofed all the adjoining walls in our house when we moved in as the walls were paper thin. We were doing it as part of wider renovations to our property as beware it is expensive and messy and you will slightly reduce the size of your room.
We researched online and bought a sealant called Green Glue which is a bit like decorators caulk or the sealant you put round the bath and is supposed to have sound proofing qualities. You seal your floorboards and fill in the gap where the skirting board is and any gap between walls and ceiling.
Then our plasterer built a new stud wall along the adjoining wall about 7cm into our rooms and stuffed rock wool (the stuff you insulate your loft with),then covered it with acoustic plaster board, plastered over the top and then we sealed in the cracks etc again with the green glue.
You then stuff more rock wool up against the adjoining wall in the loft.
Like I said we were modernising our property so we also had each room completely skimmed by the same plasterer so hard to say what it cost just for the soundproofing, we paid £1000 per room for Labour and materials including all the plastering.
It reduced the sounds about 30% I would say, so not amazing, but just took the edge off, and gives us more privacy too. Can still hear them walking and banging around, dogs toe nails scratching the floor and windows, whistling or singing, and hear the sound of conversations and some words, but can only really discern the exact words when they're shouting. We can hear their tv and feel the vibrations still as it's attached to their wall, but it's quieter. So a bit like hearing them underwater, only bit louder.
The other downside is that we can't ever drill anything into the plaster boarded wall as if you pierce the board it obviously means the sound can get through as will break the seal. So no picture hooks, shelves or securing furniture to the walls, which is a bit restrictive.
I still think it's worth it, but there is no miracle cure. We did upstairs and downstairs and it got progressively better as each room was added on, the first room on its own wasn't as effective.
Sorry for the long post, I hope you find a solution that works.