Hi izabella135
Welcome to the Apple (user-to-user) Community.
Re: What can I do when an app says "there is a billing problem with a family member's pervious purchase."
View your purchase history for the App Store, iTunes Store, and other Apple media services - Apple Support
Re: " I only get that message for when I try to redownload this specific app,"
Seems like that app may have been purchased by the family member who has a billing problem in their Apple ID account. I may be wrong.
How to see what you were charged for:
If you see 'apple.com/bill' on your billing statement - Apple Support
Re: Anyone know how to fix this?
Seems the family member (or a parent) needs to straighten out their billing problem so things return to normal.
If a message says 'billing problem with previous purchase' or 'verification required' – Apple Support
Or if you are the "family organiser" and pay for family purchases, you might need to check if your payment method has a valid expiry date, or if a new payment method needs to be added ... ie: to cover an amount owing, or for ongoing subscriptions.
What to do:
If you need to change or update your Apple ID payment method – Apple Support
How to: Add a payment method to your Apple ID - Apple Support
If there is money owing or active subscriptions,
if needed: add a new payment method, before deleting an old one.
How to: Remove a payment method from your Apple ID - Apple Support
Else:
If needed:
You might want to reach out to the Billing Support Team:
Find answers to your questions about purchases, subscriptions, payments, and billing:
Subscriptions and Billing - Official Apple Support
All the best :-)