Your main mistake was creating a new account instead of trying to recover the information for the old one. If you have a lot of things you purchased with the old ID you may wish to revert to the old ID because you cannot transfer them to the new ID.
If you forgot your Apple ID
https://support.apple.com/HT201354
If you forgot your Apple ID password - https://support.apple.com/HT201487
What to do after [or before] you change your Apple ID email address or password - https://support.apple.com/HT204071
If you still need help:
Contact Apple for help with Apple ID account security "This article provides country-specific Apple Support contact information for customers seeking help with their Apple ID password or other security-related issues."
https://support.apple.com/HT204169
or
Contact Apple for support and service - "See a list of Apple phone numbers around the world." - https://support.apple.com/HT201232
If you want to use the new ID your mother will have to invite you to the family with the new Apple ID.
Set up Family Sharing - https://support.apple.com/HT201088 - "Invite people to join your family"
Get an Apple Music Family subscription - Apple Support. - https://support.apple.com/HT205595 - including how to invite Family Sharing members