I had bed bugs earlier this year. It's not so much physical as it is psychological. They can tell when you're asleep by the change in the co2 level in the air so that's when they usually feed. Some of them will journey onto your bed in broad daylight and that's how most people know that they have them.
As I was saying though, their bites didn't make me itch, but they stressed me out to the point that I was scratching like a crackhead in school and looking over my shoulder at night. I developed rash for some reason also on my face, arms and chest and I never get those.
Roaches bite btw