I pay for more space in my iPhone but it keeps telling me that my storage is full

It is not possible to buy more storage for an iPhone; it will never have more than it did when you bought it. What you bought is iCloud storage that is used for backing up and also for syncing to other devices. Here is an explanation→What's the difference between device storage and iCloud storage? - Apple Support

iCloud+ has 2 independent functions. iCloud backups, and iCloud sync. It’s confusing because they both have the same name prefix. But they have no connection with each other. Go to Settings/[your name]/iCloud. You will see a bunch of switches (with iOS 16 also tap Show All). When you turn on a switch that data type will sync to iCloud. If you do this on multiple devices that share an Apple ID the selected data will sync to all of those devices. 

You can also turn on iCloud Backups. This will back up your phone every night if the phone is plugged in, connected to Wi-Fi and locked.

But note that anything that you sync by the first method will be excluded from the iCloud backups.

yazmin73 Said:

"I pay for more space in my iPhone but it keeps telling me that my storage is full"

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Troubleshooting an Phone Storage:

Clear Space, as System Resources may be Swollen Up:

Troubleshooting iPhone Storage:

Internal storage cannot be upgraded. It is what it is. So, the maximum internal storage capacity never increases, even if you upgraded your iCloud plan.

So, what to do...

Clear Space Using my User Tips:

• How to Clear Space from your Mobile Device, and What to Clear: - User Tip. You may have too much installed, and need to clear space. So, see my user tip: 
• How to Clear "Other" in your iPhone's Storage - Use Backup - User Tip. Caches would be being used for remembrance of application use. It is essentially the same for an iPhone. You'd backup your iPhone, and then restore your iPhone from the backup you've just created. All System Data will delete.