Hi, and welcome to the community!
Please note that premium can take a little time to activate across all devices.
Try reinstalling the app, often seems to help.
Does Spotify desktop say 'Spotify Premium' at the top?
Also double check that you're logging in with the right account. It's very easy to have a Spotify and facebook account, and if you activated with facebook, make sue to login with facebook!
Just to confirm, you can Check out your subscriptions page if you want to make sure you have premium all set up.