Please keep in mind, Pandora accounts follow the email address, not the device or phone number. You can sign into the same Pandora account on any computer or supported device, as long as you use the same email address and Pandora password. This applies to both free and paid Pandora accounts.
This also means that your collection should be available to you when you sign back into your account - as long as you're signing into the same account.
Could you tell me a bit more about what is happening?
After you downloaded the Pandora app again, were all of your stations missing?