purchased song on itunes doesn't appear on my "music" in my iphone

How are trying to redownload it, you are going to the Purchased tab in the iTunes Store app on your phone ? The 'Transfer Purchases' copies purchases (that are currently on the device) to the computer's iTunes library, it doesn't copy purchases to the phone.

Is the song explicit, and if so have got explicit content restricted on your phone (Settings > General > Restrictions) and on your computer's iTunes (Restrictions tab in Edit > Preferences) ? On your computer's iTunes to redownload music you go to the Purchased link under Quick Links on the right-hand side of the iTunes store homepage - as well as checking Purchased on your phone you've also checked there ?

On your original post you said 'the button is grey' - which button and where ?

And on your computer's iTunes it shows on your account's purchase history (Store > View Account > See All to the right of the Purchase History section), and does it show (with a cloud icon against it for downloading) if you go to the My Music section of your library and enable 'Show iCloud Music Purchases' via the Store drop-down menu :

The cloud icon being greyed out, and the Purchased or Play buttons being greyed out, implies to me that it's being blocked due to a restriction - is the song labelled as explicit in the store (here in the UK explicit music has a red E on it) ? 'Play' indicates that it's currently downloaded into your library on that computer, 'Purchased' means that it's been purchased but isn't currently downloaded.

(For the 'show iCloud music' or 'show iCloud music purchases', Apple seems to frequently rename settings/options, it should be/do the same thing.)

Have you purchased any other explicit music and, if you have, can you play them or redownload them from the store ?

In your first post you also said that you had tried to 'hide and unhide the song' - did you hide the song, and you then unhid it ?