Link Dot to Prime Music

[DocPaul]

Hi gang.
 I'm a newbie to the site and I'm sure this question has been asked many times.
Please provide me with a link to the post(s) that may help or a solution to my problem.  Thanks.

Here is my problem:
I have a Amazon Echo Dot ( purchased 12 - 2017) and set it up. Works fine, then I purchased Amazon Prime (full year subscription).  I downloaded AmazonAlexa and Amazon Music to my Apple 5S phone.
If I ask Alex to play a song ( "Pinball Wizard by the Who") I get "Here is a SAMPLE of Pinball Wizard by the Who", not the whole song.
What step(s) have I missed to link the Prime to the Alexa ?
Please advise.  Thank you in advance.

Doc.

[Laurel]

If you don't have Amazon Unlimited, you will get that message for certain songs.  I am in Canada and we don't get Unlimited so I am familiar with the message.  But in the States you have to buy into Unlimited to get a larger range of music. 

[fstbusa]

as stated above, some songs are not available with basic prime