Hot and humid means bugs, no different in Florida. True cockroaches can infest,breeding and living on their own waste. Sad you have a fear of them, they are harmless,one of natures little animals, just pest in numbers. They live anywhere, clean just means less germs they may spread. Numbers? I have seen a thousand living in a VCR. An exterminator won't be cheap and results only short lived. Your call though. They come out at night, perhaps take a peek then, You can put down a little boric acid where you see them crawling most.
Roaches are not my favorite bug either, Just soon not have them,bedbugs are far worse.A hint, bet you have spiders too, don't kill them,they are the best natural exterminator you can have next to house centipedes if you can tolerate 8 or 30 legs at all.
30 days you could just stick it out, get used to the buggies and your anxiety wanes.
Hope this helps.