If you're visiting the App Store on your phone and you see an OPEN button, then the Pandora app is installed on your device but not be installed on the home screen.
Try visiting your iPhone's App Library and enter Pandora in the Search field to see if it appears. If you're unfamiliar with the App Library, please visit Apple's Find and use your apps in App Library on iPhone.
If the app is not showing up using after running through the above, check whether you have any age restrictions set on your device. Pandora is "unrated", so if you have some restrictions set, it won't appear even when installed.
Hope this helps!
