how to prevent mold from spreading into new apartment once I move

hi all, this could be the wrong subreddit, and if so, please feel free to delete/etc.

long story short, I've been subletting a basement apartment for about six months, and it got pretty moldy down here once it got warm and humid. The new apartment I'm moving to is on the second floor, it has no mold or moisture problems. I'm not worried about the new place, but I am worried about creating a new mold infestation once I move.

A bunch of my possessions got ruined by mold when I was storing them in the crawlspace, and I've trashed them, so no worries there. But, I've kept my clothing and mattress down here, and I'm not about to trash them, unless I'm convinced beyond all doubt that it would condemn my new space to moldy hell.

I was wondering if anyone else has been in a similar situation before? How did you manage to move your stuff to a new place without bringing mold with you? Should I even be worried if the belongings I'm bringing with me aren't visibly moldy?