Ok listen .. I paint for a living and you’re getting some really bad advice from everyone. what you’re seeing aren’t nicotine stains. Nicotine stains on ceilings are more like an even brown film that builds up over time which turn the whole ceiling from bright white to a nasty pale tan color. If that were the only problem oil based Kilz is the way to go. Nicotine stains don’t leak. What youre seeing are water stains.. they are gross brown spots that appear on ceilings when there is a moisture problem inside the walls or ceilings...and by the looks of it I’d be willing to bet you either have a bathroom directly above yours that has’t been properly maintained or if you’re on the top floor the roof needs to be replaced. Here’s some things you can do to diagnose the problem.. 1. Look at the condition of your flooring. Chances are in rental buildings with multiple units your upstairs neighbors will have the same finishes you have that are in similar conditions. If it’s tile make sure the tiles aren’t cracked and there isn’t any cracked grout between tiles. Sheet Laminate.. pull up a corner of it behind the toilet if it isn’t curling up already and check for mold and moisture on the sub flooring. The positioning of the water spots makes me think the floor boards above you need to be replaced and that there is ceramic or laminate tiles that water is seeping in around the corners into the floor boards above you. Which also may need to be replaced.
I would not keep scrubbing the ceilings with TSP. It’s probably hurting more than helping. Do not prime the ceiling before the water leak is dealt with. You have a moisture problem that your slum lord most likely knows about and keeps trying to temporarily fix to keep rent money coming in. This isn’t something you can fix yourself unless you know a lot about rehabbing buildings. I assure you there’s mold present that needs to be dealt with. Maybe lead paint flaking off depending on the age of the building..who knows. What I do know is the quickest way to get it fixed is to stop paying rent until your apartment is up to code.