Is your account showing as premium (not unlimited) on your online overview?
If it is showing as premium then you should be good to go! Sometimes a quick log out and back in again is needed. If you are still having issues, try a clean reinstallation of the application.
If your account is still showing as free then you have not logged into the account you have upgraded. Double check your details, its amazingly easy to accidentally have two accounts, one with a Spotify username and another using your Facebook details. If you can't find your account, don't subscribe again as you might be billed twice, instead get in touch with the customer services team directly using the online contact form and they will be able to lend a hand.
If you get an automated email reply back directing you to the community or help pages, you need to reply directly to that email (even if its from no-reply) and one of the customer services agents will get back to you as soon as possible.
Alternatively, if you prefer support via Twitter, please tweet @SpotifyCares.
It sounds like you might have two seperate accounts. The one you're using on your iPhone is a free account and the one you're logged into on your laptop is Premium.
A duplicate account created through Facebook is a pretty common issue and can be easily resolved by contacting Spotify support though this contact form. If you receive an automated reply back then just reply to it and you will be put through to a Spotify representative.
Don't worry, you'll soon be enjoying Premium on your iPhone if you follow these steps! :)
If you are using IOS, you may want to open multi-tasking (double clicking the home button) and close the app, by either holding the app and pressing the red delete button for IOS 6 or earlier, or swipe up for IOS 7 or later.
Have a musical day!
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