Discharged from a small group home, having a hard time finding another facility in NC. What are the laws?

Discharged without seeing that you had a safe place to go? A nursing home can't legally do that, I would think the same would apply to group homes.
Whether or not you feel something from the Adult Care Licensure Section applies to your case, call the Department of Health (919-855-4500) to see if you have grounds for a complaint and assistance finding a new place.
https://info.ncdhhs.gov/dhsr/acls/overview.html

South Carolina has a Lot of Facilities if you can't find anything in NC try the Charleston Housing authority - supposedly they have Good elder facilities .