What kind of disease, illness, or allergy could I have?

Over the past day or two, I've developed what look and feel kind of like mosquito bites, except they don't itch as much and aren't as big. There are about 5 of them now all over my body, and there are no bugs in my house.
im in a cold climate in ny, and i live on the 7th floor
also the mosquito bite things don't appear at all until i accidentally scratch the area they're in

Could be some sort of bug bite like spider, ticks, bedbugs or fleas.

Sounds like mosquito bites, regardless.
Two things you may want to consider... hatching spiders (almost too small to see) or bedbugs.. one other possibility is dust mites.
have you changed the brand of laundry soap, fabric softener, or body wash that you are using lately? if so you could be sensitive to the new brand. are you taking a new medication either a prescription or an over-the-counter? or have you recently (within the last 30 days) adjusted a dose of medication? if you you may be reacting to the medication. even if you always could take a certain medication in the past, you can develop a sensitivity to it. you may have come into contact with something that never irritated your skin in the past, but is now causing a problem. have you made changes in your diet? maybe you are sensitive to something you ate? in any event, you should probably go see your doctor and they can prescribe something to help with the itch. hope you feel better soon.