Itunes store won't let me download my album

You have purchased the album.

Click Music.

Then check again -> Music Libary -> Recently added.

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See also the following Apple articles:

View your purchase history for the App Store, iTunes Store, and other Apple media services

View your purchase history for the App Store, iTunes Store, and other Apple media services - Apple Support

Redownload music in the iTunes Store app on your iPhone, iPad, or iPod touch

Redownload music - Apple Support

If there's an issue when you re-download apps, films or other content from Apple

If there's an issue when you re-download apps, films or other content from Apple – Apple Support (UK)

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If you can't see the item that you want to redownload

• Make sure the item is in your purchase history for your Apple ID. If you can't see the item in your purchase history, you may have purchased the item using a different Apple ID.
• If you can't see an app that you want to re-download, that app may not be compatible with your device. For example, an app that you've bought for your Mac may not work on your iPhone or Apple Watch.
• If you can't see items in your purchase history on other Apple IDs, the purchases might be hidden. Find out how to re-download hidden apps or unhide music, films, TV programmes, books and audiobooks.
• Do you want to re-download an app or other content that a family member has purchased? If you use Family Sharing, you can download shared purchases.

If there is a problem when you re-download

• Find out what to do if you can't download any apps on your iPhone or iPad, or you can’t download any apps on your Mac.
• Can't connect to the App Store, iTunes Store, Apple Books or Apple TV app? Find out what to do if you can't connect.
• If you see items in your purchase history but you can't re-download them, report a problem.

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If you have received an invoice from Apple, tap on Report a problem on the invoice.

How apps, content, and subscriptions from Apple are billed

How apps, content, and subscriptions from Apple are billed - Apple Support

If you still need help, get more help and assistant from Apple directly, see Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK)