I selected "yes" for paying for childcare and selected that my child lived with me. However, it is not allowing me to enter any amounts paid.

Are you trying to get to the dependent care credit section of TurboTax?   Or are you getting an error message?  

How do I get to the Child and Dependent Care Credit in TurboTax?

Who is a Qualifying Person for the Child and Dependent Care Credit?

It's not clear what section of TurboTax you are in, because the child care section does not ask whether the child lived with you. You specified that in the Personal Info or Your Info section.

If you are trying to get the child and dependent care credit, have you entered your income (and your spouse's income if you are married filing jointly)? You cannot get the credit unless you have income from working (a W-2 or self-employment). TurboTax will not let you enter child care expenses if you don't have income from working.