I chose to not claim the additional child tax credit but it is still asking me to put down my child's provider name. She only went to public school, did that count?

You are confused about the child-related credit you are asking about.  You must be referring to the child and dependent care credit.  If you did not pay someone to take care of your child so you could work, you cannot get the childcare credit.  You need to remove that form.

https://ttlc.intuit.com/questions/2580507-how-do-i-delete-form-2441-in-turbotax-online