Hello. I am sorry to hear that your cats are having some trouble. My name is ***** ***** I have been a veterinary nurse for 26 years. I would be happy to help.
If your cats have some type of bug that is also biting you then the most likely causes would be
1. Fleas. I would remove the flea collar. These are ineffective against fleas, can cause skin irritation
and allow you cats to breath in pesticides 24/7
2. Cheyletiella mites also known as walking dandruff. The link below will cover this in more detail
3. Sarcoptic Mange mites which can cause scabies in humans.
Now things like bed bugs can and will bite both humans and animals but animals are not a typical host for this type of bug.
The only way to properly identify what type of bug this is would be to have your vet take a look at one of the cats.
Your vet will carry a topical medication called Revolution which will kill off all of the types of parasites listed above.
Without knowing exactly what we are treating there is no way to know if they are coming from the rug or some other area and exactly what is needed to treat the environment to stop the problem.
I hope this helps give you some ideas on what may be going on.
Please reply back if you have additional questions. If you do not need further assistance please provide a rating before exiting the site so I am compensated by justanswer for assisting you.