The old woolly bear problem (and I'm not talking about JB

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As mentioned check for any other potential problems such as rad leak but it does sound like a woolly bear infestation.
Wooly Bears are the larvae of the carpet beetle and they feed on natural fibres such as wool.They are found along the edges of the room, as people don't tend to vacuum right up to edges on a regular basis they can thrive here.Also look under heavy furniture you may also find bald patches here.
Also look for the beetle trail across the carpet, alot of people think they that a slug has got in but it is in fact the wooly bear.
The problem is easily transported by clothes,shoes,rugs brought in etc, so airing cupboards have to be checked as well.
You could try a product called Patriot C which is perfectly safe and you will have to treat carpets front and back.