I think they didn't do a proper job of abatement after the flooding problem. They didn't ensure that everything was dry. But then after flooding you should replace sheetrock, not hope for the best.
Checking for sheetrock. Most apartment complexes have it. Either that or they are using a concrete block wall. If you rap it with your knuckles, and it goes knock knock knock, and you don't hurt yourself, it's probably sheetrock. Also, if you can drive a nail into it.
Can you put your finger through the wall? Even if it's sheetrock, it shouldn't allow you to do that. If it even feels soft have it replaced.
Sheetrock acts as a wick when the floor is flooded. And then as a sponge after the water has drained. Paint only hampers the drying process.
I had a problem similar, but it was on the front wall of the living room, not in a closet. The gutter upstairs wasn't draining properly, wasn't installed properly, so water would run down the wall. Eventually it soaked the inside wall, and I could put a finger through the wall. So they replaced the gutter system, and then re-sheetrocked the inside of my living room wall. Re-painted with Kilz primer, then interior latex housepaint. Eventually we got the carpet replaced.
Chlorine bleach has been used in household laundry for a century or so. The only problem is as Wuntvor stated, mixing it with ammonia, which releases deadly chlorine gas. So don't go spilling any in the cat box!
If you have mold, you have spores. The only good molds, are the ones you eat.
It isn't so much that vinegar feeds mold, it just isn't very effective at killing it, and if it doesn't kill you it only makes you stronger, is how mold acts. It is a decomposer or organic material, and vinegar is organic. Chlorine isn't so much organic. Although you need some to digest your food. But that is what table salt is for.
Also, have them fix the bedroom heater. In fact report all problems to be fixed. A broken heater may be the cause of a fire later on you know. It may not be so much broken, as a wire is loose, which causes the fire.
Keeping the room dry and to a normal warm temperature will do a lot for making mold more tolerable.