Hey there GTSB_24,
Thanks for reaching out to Apple Support Communities. I understand you and your mom’s data is syncing between your devices unexpectedly. I’ll be happy to help.
The best way to prevent this from happening is for one of you to create your own Apple ID so that your photos, reminders, and sync with a different account than your moms:
How to create a new Apple ID
One you've created your own Apple ID, you'll want to sign out of the ID that you both share and then sign in with the one that you've created. You can follow the steps in the following article to sign out. Be sure to select to keep a copy of your data on your iPhone when signing out so your data is not deleted:
Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac
You can also set up Family Sharing so that you easily share photo streams, purchases, and more between one another. This article has more details:
Set up Family Sharing
Regards.