How to stop messages on an IPhone 5s to sync to another device?

My mom updated her phone today, and ever since all my messages on imessage have synced to her. We have the same account. And its only my friends messages being sent to her. But id like my privacy and so does she and we need to know how to make sure both of our conversations arent seen AT All and that if we were to figure out a way. We can still get notifications on our device alone. I found a way by turning imessage off but i hear that it will cost extra since its not on the data plan and since i've turned it off i haven't been able to get a single vibration or notification that i've had one. So i need help.

You both need to have 2 separate Apple IDs. That is the only way to make sure that your messages don't share. Either that or make sure family sharing and/or sync across all devices is turned OFF.

Just make a separate Apple account from your mom's. Factory reset your iPhone and set up a new iCloud account. Then sync with iTunes to get back settings and contents.