Yes, chiggers can live in the carpet, etc. Rather than using a bomb (as taddyport mentions, you have to clean everything afterwards), try using Zodiac Household Spray. It's a flea and tick spray meant to be used on upholstery and carpets. Check for color fastness (spray in a small corner to make sure it doesn't discolor, etc.). Then spray everything that can't be washed - mattresses, cushions, blinds, floor. Spray into corners.
For fleas and ticks, you would repeat the spraying in 2 weeks to kill anything that hatched after the first spraying. I'm not sure of the life cycle of the chiggers, but a second spraying won't hurt.
I have used this stuff on chiggers and it killed them.