Thanks for reaching out about this here in the Community.
You and your sibling should be able to listen to your music on your own separate devices at the same time, as you're using your own separate accounts.
If the streaming from one account is interrupted when the other person starts listening to music, it means that you're both logged in to the same account. In this case, we suggest following the steps under Log out everywhere in this article. Then, log back in making sure you're using your own account's credentials.
Let us know how it goes.
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“Music acts like a magic key, to which the most tightly closed heart opens.”– Maria von Trapp