Spores

Hi everyone, I'm new to his forum and I've been having a problem with mold in my apartment for a while.

It all started after a pile of clothes and some cardboards on my balcony got wet and a while later I found a few black mold stains on one of the garments. The stains were not the kind that can be brushed off, but looked like a discoloration. The rest of the clothes smelled from mold but did not show any stains. I threw most of them out and put the rest in sealed bag.

Since that happened, mold seems to develop very easily in my apartment as soon as anything gets wet or even humid.
I imagine this is because there are now many spores floating around, and that is my problem.

I have read what the mold experts say, and according to most of them it is possible to kill mold but NOT the spores.
If that is true, it would mean that I would either have to live with the increased amount of spores or leave the apartment. Inhaling mold spores cannot possibly be a good thing.

What say you all? I keep the apartment clean and if I see mold I immediately throw the affected item out or clean it with bleach. But if I have an increased amount of mold spores floating around this may be a losing battle,
unless I can kill the spores too.

Any advice on how to proceed is most welcome.