How do I switch emails on Apple Music on my iPhone?

If you created a new Apple Account, you’ll need to export and import your playlists, and buy new subscription, and, discontinue your subscriptions, as purchases are generally tied to an Apple Account.

More common would be to modify the email associated with the Apple Account, as that will preserve purchases, photos, iCloud data, playlists, and the rest: Change your Apple Account primary email address - Apple Support

There is a limited means of moving purchases: Migrate purchases from one Apple Account to another Apple Account - Apple Support

The Apple account for Apple Music on an iPhone is the one logged in, in Settings ➜ Account ➜ Media & Purchases.

You can sign out of that account, and sign in with the new one if you want.

Do note, it will also change the account for the App Store, iTunes Store and iBooks Store on the iPhone.

Also, media purchases remain tied to the account that made them as do subscriptions, so if you change the account to a new one, you will want to cancel all your active subscriptions otherwise it will continue to charge you on the old account.

Also, as noted by MrHoffman, did you change the email address for your Apple account, or did you create an entirely new one?

Or are you wanting to update the email address used for your Apple account?

Depending on what you did, or want to do will be what steps you need to follow or what can be done.