Oh dear . . . the cockroach is the official state animal in Florida. :P We lovingly refer to them as "palmetto bugs." I've seen some the size of teacup doggies.
I would check with my exterminator. Every couple of months our guy sprays something around the outside perimeter of our house and that seems to keep them in check. Our house is pretty clean, but we live on water (which attracts them). It's good to keep all paper and cardboard out of the house (they love paper products). And of course don't leave food laying around.
My boys laugh when they see me run off with a broom and dust pan to engage in epic battle with a cockroach. They are very quick unless they've gotten into poison. And beware cockroaches on their backs - if you turn them over they will miraculously revive back to life. When I catch them I flush them.
I've also read to sprinkle dimataceous earth around spots where you see them. I'm about to do that in my son's closet.
Once I threw one in the canal behind our house . . . I kid you not the thing started back-stroking for the shore.
Cockroaches will truly inherit the earth.