The problem I’m having is that my sister subscribed the family sharing for all of us buy yet we were still asked to pay for the Apple Music, how can I enable the family sharing without having to pay again?

Did your sister make herself the Family Organizer and follow all the steps in:

Set up Family Sharing - Apple Support

Get an Apple Music family subscription - Apple Support

and did everyone else accept the invitation from her?

If so, you might be able to fix your issue by turning Sync Library off for all of your devices, then turning it back on again.  Learn how.

Also, if you are now subscribed your your own plan, you won’t be able to get invited back into the family plan. You’ll need to can el