I had paid for a storage plan and it won’t let me use it.

You can't buy more storage for your phone, it is a fixed size. You bought iCloud storage which is used for syncing data between devices.

iCloud is where you offload what won’t fit on your device, as you manage your available local storage.

Your device storage won’t increase.

All iPhone, all iPad, and many Macs, will have what storage was shipped from Apple, and cannot be increased.

What's the difference between device storage and iCloud storage? - Apple Support