Hello ! Well I've contacted Apple Support but they told me to get in touch with Tech Support and I just gave up, especially since I'm 90% certain what I did worked. Apple Music works just fine, for both me and my family members, I can still get both free and paid apps for myself using my credit card, and I've tried the App Store from my mother's phone to see which account would be used and it was using hers for both paid and free apps. I didn't actually go through with a purchase from her phone, hence the 90%, but any transaction was going through her account and there was no mention of mine or Family Sharing so I think it's ok.
Selecting the "Stop Family Purchase Sharing" option only does that one thing - it stops the sharing of music, movies, TV shows, books, and apps.
It does not change the dynamics of how the billing for a Family Sharing account works. The only way to prevent other Family Sharing members' purchases from being billed to the Organizer's account is to have the family members purchase an iTunes card and apply it to their accounts.
If a Family Sharing member's account has a credit balance on their account, the purchase is first deducted from that credit balance. If the purchase exceeds the available balance, the remaining amount is charged to the Organizer's credit card.
If any Family Sharing member is under the age of 13 (where Ask to Buy is required), or any Family Sharing member that has the Ask to Buy option turned on will have all purchases billed to the Organizer. Even with an iTunes & App Store credit balance, if Ask to Buy is turned on, the purchase will be taken from the Organizer's credit card.
Had you completed the purchase on your Mom's iOS device, you would have been able to verity that the purchase was charged to your credit card. There would not be any mention of the fact that your card would be charged since that is the way that Family Sharing is set up to work.
The only way to prevent purchases from being billed to your account is for each of the Family Sharing members to have an iTunes & App Store credit balance, which is achieved by purchasing and applying an iTunes Gift Card to their Apple account.
See the "About Family Sharing purchases" in this support article: How iTunes Store purchases are billed - Apple Support