Hi there! I know a thing or two about bugs. First, I'm about 99.9% sure you do NOT have bed bugs, termites, or carpenter ants. Hoorah!
The photo is unfortunately a little blurry, but if I were to make an educated guess, I'd say you found a deposit of shed skins from beetles, specifically some species of carpet beetle such as the black carpet beetle (the adult beetles are black, not the larvae). You mentioned being in New England. Here's the extension services page on carpet beetles from the University of Maine:
https://extension.umaine.edu/ipm/ipddl/publications/5008e/. Look at the larvae in the colored picture and see if that matches what you found. You can also look for adult beetles around your house, most likely at the bottom of your window sills, or on the floor just underneath the windows. Carpet beetle larvae do not like light, so tend to hang out under the edges of carpet or wooden moldings, or in closets, where humans won't disturb them.
Someone else mentioned silverfish, but I think that's unlikely. The body shape is similar, but the skins you found are the wrong color and have stripes. Also, silverfish are known cannibals, so it actually would be unusual to find a big cache of skins like you did.
It sounds like you already cleaned this spot up, but if you find more skins, put some in a sealed clear plastic bag and you can show it to an exterminator if you want an ID.
Anyway, what should you do about these probably beetles you found? Not much, actually. Carpet beetles don't bite or spread disease to humans, though in large quantities their skins may upset someone's allergies. They can chew holes in natural fibers, however, like in rugs or clothes. Cleaning the area was the right thing to do. Change your vacuum bag if you haven't done so already. No need to set anything on fire. In the future, keep cleaning your house regularly to minimize the food carpet beetles would have, such as hair and dead skin cells on the floor. The U of Maine page has more details.
