Hi, DL_2020!
Thank for stopping by the Apple Support Communities to get help with your contacts. It sounds like you see your mom's contacts on your iPhone, and deleting contacts on your device also deletes them from hers. You've come to the right place for assistance!
We understand that you and your mom have separate Apple IDs. This is good, however the only time contacts can be synced is when the two devices are signed into the same Apple ID. We encourage you to double check where you're both signed in, just to be certain: Check your Apple ID device list to see where you're signed in - Apple Support.
Best.