Q: Purchased album on iTunes downloaded on my iPhone but doesn't show up as Purchased on my iTunes Account

Hi BirdsInTheTrapSingMcKnight!

I see that the album you've purchased on your iPhone is not showing up as having been purchased, though you have the album in your Music app. It sounds like you are also unable to download the album on your PC as well.  I can understand why this would be a concern, and I'm happy to help.

The first thing I would recommend would be to sign out of the iTunes Store on your iPhone, then sign back in.  You can see instructions on how to do this below. Keep in mind that signing out of iTunes and back in will remove any music downloaded for offline listening if you're an Apple Music member. You'll need to re-download those songs again. 

Sign in to the iTunes Store on your iPhone, iPad, iPod touch, Mac, PC, or Apple TV​

Using that same link above, you can verify that you're signed in to the same Apple ID on your PC.  Once you've done that, you can use the following instructions to view and download any iTunes Store purchases:

Download your past purchases

Thanks for using Apple Support Communities.

Cheers!

Since that didn't work, it would be best to contact Apple to speak with the iTunes Store support team.  You can use the following link to get in touch:

Apple - Support - Product Selection