About what size piece did she ingest? My chicks (and later chickens) have eaten various things that I thought might be harmful - chunk of fruit peel, small piece of plastic on the lawn, piece of the daughter's craft yarn, etc. They never had any issues with any of it. Unless it was a fairly large piece of cotton, I would think she should be fine. Offer some chick grit to help in grinding it down in the crop. Keep an eye on her, and if she continues to eat, drink, and eliminate waste, she should be fine.
how big was it ? hows she acting ? animals eat a lot of things they sometimes shouldnt.... watch her and provide lots of water . if she starts acting funny or not eating . then id take her to a vet she may be blocked