Yes, I've gotten a runny nose and itchy eyes from handling stored fabric. Just happened yesterday, in fact.
Scraps can be washed. I've done it many times.
You can get a lingerie bag and put them in that and toss it in a washer.
or
You can wash them by hand in a basin, sink, big kettle - rinse them - I use a colander if the pieces are little -
lay them out on towels to dry.
Depends on how much you want to keep and use the pieces.
The main thing would be to wash like colors together in case one of the pieces is a bleeder.