My child was abused in a facility and the staff was arrested can I sue

Probably yes. If this took place less than three years ago, it was a private facility, the abuse was serious, and it took place in the course of the staff person performing their job, the facility is responsible, and you may have a case.  If the facility was run by a government entity, you had 90 days to serve a notice of claim in order to preserve your right to sue.