One (1) cockroach, and I torch the place & pitch a tent.

So I don't know if my situation is similar, but I recently moved into an apartment (about three months ago) and this is the first time it has been cold enough to have our windows closed. Now everything feels slightly damp and... just a little off. Mainly I have noticed this is with clothes and books, even if the clothes are hung up. This doesn't happen if the windows are open. Is this mold or is this something else?

Damp Rid works pretty good for the "damp feeling." That helps before it becomes a big mold problem.

FWIW, if you have books that are slightly off, you can microwave them (spread the pages open) for about one minute. DO NOT put them in with other books until you're sure they're okay.

We have an older microwave at the office that we use just for that.