New phone is receiving text messages from my mom under my number

My family and I recently got new iPhones and transferred our data from old phones to the new. My parents have their own Apple account that they share, while I have my own. I did use their ID to help set up my phone because some of my apps were downloaded when I was still part of their account (tried to set up a new phone without that step before and ended up with half my stuff missing). Today, my Mom texted me and the message appeared on my iMessage thread with myself. Basically, if I don’t want to forget a link or something, I’ll occasionally text it to myself so I can easily find it later. For some reason this thread now has the texts sent from me going to my mom instead of going to me. We’re both very confused, especially since the text thread between her number and my number is still working (i.e. I can text “Mom” and talk to her in that thread & I can “Me” and still talk to her). Any help would be appreciated.