Yeah, pretty sure you're both signed into the same Apple ID for iMessage. To deactivate that on your phone, you can go to Settings -> Messages and remove your mom's info.
Messages is very useful though, it can really cut down on text message costs if you don't have unlimited. To learn more:
Yes it sounds like you have her iCloud Id signed into iMessage. Like the poster above stated go to settings/messages/send and receive and sign out of iMessage.
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Oops also meant to tell you to sign back in with your Apple ID