I live in a 2 bdrm duplex (about 30 years old) and my upstairs bathroom sink is backing up primarily when my neighbor who also owns the property uses their sink. I can hear them plunging it out sometimes and my side starts to back up and spit black sediment and sludge. I have tried draino and it no longer clears the drain and plunging it does no good anymore. The drain is almost completely clogged and barely drains even when I use the sink. The other night it backed up almost to the top edge of the sink and I am afraid eventually it will overflow all over the floor.

You might have to ask the owner to snake out the main clean out pipe, because there's a good chance there connected on same pipe and that's why you hear him plunging it too, because his side is plugged up too. I'd have him do this as soon as possible before something of yours gets damaged.

It's not the main that needs to be snaked but the lavatory roof vent is the one that needs the attention. Put out enough cable to reach the base and 15 feet more. It's the owners responsibility to insure that your drain lines are clear. By plunging his lavatory and pumping the crud up into yours he is inflicting a hardship on you. Have him correct it at once. Good luck, Tom