it will appear in the Purchased Playlist underneath the STORE in the side bar.

That song is also in the Library! It has to be, as that is where ALL the playlists get their information from.

In the Sidebar, click on Music and then search, top right of iTunes window, for the name of your song.

You cannot UPLOAD a song on iTunes but you can DOWNLOAD a song from iTunes
you can IMPORT a song into iTunes.

Which one of the above did you actually do? Either way, whatever you Import or Download will be in the Library.