Dear Ty - These most likely are nuisance pests known as household casebearers or plaster bagworms - see http://tinyurl.com/ykbhp9y for an image. These cases are constructed by larvae (caterpillars) of
DS, Is it possible that this is not an insect or mite, per se, but rather some type of allergic reaction? The key phrase you used was "new job" which probably means you are spending a lot of each day
Dear Carina - These do not look like eggs of any kind; what it resembles most is a small critter, such as a larva of some kind, that died there, and now has been colonized by fungi. I would just try cleaning
Dear Carina - Could you please take a photo of these and attach the image to a follow-up question? I doubt very much that these would be moth eggs, and even if they were, no pest species that I know of
Stacey, This is a perfect description of a powderpost beetle. The holes and sawdust are made when the beetle bores out of the wood. The larvae live inside for months or even years feeding on starch

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