Heather: You have a tough problem. Without really knowing how your unit is constructed, it may be near impossible to solve your problem.
Like Jay J mentioned (the kid is smart-and helpful, isn't he?) the demising wall, i.e. the %$## wall between you and your neighbor, may be part of a method of construction where there is no isolation between you and "them". If things are built with lumber, not masonry, then the usual method of construction ties everything together. That would be walls, floors, and ceilings. Whatcha got, kiddo, is a drum. ("They" probably have their stereo hanging on that wall too, don't they?) Therefore, sound generated in one part of the building can be transmitted to other parts via the floor, or the ceiling, or the walls, or right thru the wall studs, or, if you live with an attic space above you, and if the builder did not build a fire wall between you and "them", you can get sound traveling to visit you that way. You can "help" the situation by insulating the wall between you and "them", but odds are you will still get some transfer. Cheapest way for now is the blown-in method. Shouldn't cost too much and you can repair the wall easily. Next, you probably would have to isolate the wall by building another one next to the existing wall with a little dead air space between them. But. as I keep harping on, the fore-mentioned problems with probably come to bite you on the ankles.
You could also call upon a "specialist" (yes, people make a living doing this) and get his/her opinion. You might call your lumber yard or an area architect for a phone number. This guy might offer you some additional info on "isolation" systems that can be applied to your side of the wall. Sometimes, heavy materials (lead in the old days) is attached to the wall with additional sound isolation channels, attenuation caulking and weird stuff like that which if installed properly, could help also.
The problem I see is that you are going to spend some money and most probably not get the results you want. Surely you project has some sort of orgaization which might also have suggestions. Guess it all depends on how expensive your unit is and how much you want to spend.