You first should determone the exact construction, The wall you describe doesn't sound like it would meet current firecode requirements for multi family units. You can add damped mass to your side of the wall but if there is a direct physical pathway for the vibrations on your neighbors side of the wall to set your side in motion you will still hear a fair amount of noise. You can pull an outlet cover and shine a flashlight in and maybe get some insight on the actuall wall construction or see if you can talk to someone connected with the buildings construction.
If you own this unit and plan to stay some time it may be worthwhile to pull your side of the wall off and start over. This time using mechanical isolation techniques to minimze direct vibration transfer. (Clips and channel) then seal up any air gaps in the wall, make sure it is fully insulated, add putty pads to any exposed outlets, then hang two layers of 5/8 drywall with Green Glue. You need to assess whether there are any flanking pathways. again your really need to know the construction design.
If you own this unit and plan to stay some time it may be worthwhile to pull your side of the wall off and start over. This time using mechanical isolation techniques to minimze direct vibration transfer. (Clips and channel) then seal up any air gaps in the wall, make sure it is fully insulated, add putty pads to any exposed outlets, then hang two layers of 5/8 drywall with Green Glue. You need to assess whether there are any flanking pathways. again your really need to know the construction design.