Why are my emails appearing on my child's iPhone?

Assuming that your email is xxxx@icloud.com …

… it sounds like your child is using your Apple Account.

A child MUST to have his/her own Apple Account created by the adult Family Organizer from their own device.

THEN the adult needs to personally setup the phone for the child using the newly established “child” Apple Account credentials.

Set up Family Sharing - Apple Support

Create an Apple Account for your child - Apple Support

Use parental controls on your child's iPhone or iPad - Apple Support

And before you do any of that, you need to completely delete your own account info from the child’s phone as follows:

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

Are you and your child using the same Apple Account (formerly an Apple ID)?

If you are create a new account for your daughter.

Stop sharing an account.