Q: How can I have my own Apple ID not linked to my mums

Hello

I would suggest getting your own account

But

Link them using Family Sharing

Here are a couple links

Family Sharing - Apple Support

Share purchased content with Family Sharing - Apple Support

Doing it this way, you can still share the purchases you've made

Best of Luck

If by linked you mean you are using Family Sharing, then unless you are old enough and willing to pay for your purchases yourself, you can't.