Unable to access Apple Music on family plan for my iPhone 15

Re: Apple Music not working :

Wondering if the Music app on your iPhone opens up ok.

What to do: If a message says 'Your Media & Purchases account has been disabled' - Apple Support

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Re: "My home page will not load,

You might want to check that you are signed in to your iPhone with the same Apple Account details that the family organizer has listed for you in Family Sharing:

How to: Sign in to your Apple Account on the web or in your device settings - Apple Support

or

You may need to tap "listen now" > tap the photo icon > Then sign in with your Apple ID and password

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Re: I can’t play any music, and it shows I have nothing saved in library or downloaded.

Everyone in Family Sharing automatically has their own Library to which they can add whatever music they wish to listen to. See how to: Add and download music from Apple Music - Apple Support

For your previous purchases (if any):

How to: Redownload music from the iTunes Store on your iPhone or iPad - Apple Support

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Re: "I’m on a family plan and the owner hasn’t canceled anything but it won’t work only for my phone"

Normally, the family organizer would send you an invitation to accept before you access the family plan.

If this, or something similar, hasn't happened, you may need to check with the organizer..

More info: How to Add a family member to your shared subscriptions - Apple Support

and

If needed: How to share apps and purchases with your family - Apple Support

If purchase sharing is enabled for the family:

See: How to download apps and content that your family members purchased - Apple Support

and

See what to do: If you can't find your family's shared apps and content - Apple Support

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Music Support Website: (info. / support / contact options etc.) : Music - Official Apple Support