My messages are going to my granddaughters phone that is under me how do I stop it

If you do not want to use a separate Apple ID then, alternatively,

Disable text message forwarding

1. On your iPhone, go to Settings > Messages > Text Message Forwarding.
2. 
3. Disable the devices which is reading your texts
4. 

It's possible that both of you are using the same Apple ID. It is generally recommended for each individual to have their own separate Apple IDs.