It appears that Family Sharing was never setup properly in the first place. Your iPhone, at the time, was probably setup with your Mom’s Apple ID. In other words both of you were sharing one single Apple ID. This means that all the apps that you had downloaded while using the other Apple ID are still associated with that Apple ID.
At present, you have changed the Apple ID to make it your own, however, those existing apps are still linked to the original Apple ID (Your Mom’s). What you will need to do is to delete those apps and download them again while logged in to your own Apple ID. This will allow you to update your apps without requiring someone else’s Apple ID password.
Also Ensure that YOUR Apple ID is listed for Purchases in the App Store.
Axel F.