My texts and email are going to both mine and my mom's iPhone. How do I correct this?

Getting each other's text messages is being caused by using the same Apple ID for iMessage. One of you needs to go to Settings>Messages>Send & Receive, tap the ID, sign out, then sign back in with a different ID in order to stop this. If you're sharing the same ID for FaceTime, do the same thing in Settings>FaceTime or you'll get each other's FaceTime calls. Note: you can continue to share the same ID for iTuens.

As far as your email, are you sharing the same iCloud account? (Check Settings>iCloud to see if your devices are using the same ID.)