iCloud Storage and iPhone Storage are two different things.
iCloud Storage is in the cloud, where you can store photos, files, messages, backup etc. So not physically on your iPhone.
Storage space on the iPhone is the storage space that is built into your phone. For example 64GB, 128GB etc.
If your iPhone reports Storage Full, start by seeing which apps take up space by going to:
Settings -> General -> iPhone Storage
The list is built so that the apps that take up the most space are at the top.
You can also enable Optimized Storage for your Photos. This means that your iPhone saves a smaller version of your photos so that they do not take up as much space on your iPhone. The original photos are stored in iCloud, and there you can make use of the extra storage space you have purchased.
To turn on optimized iPhone Storage, go to:
Settings -> Photos. Checkmark in Optimized iPhone Storage. Also remember to enable iCloud Photo. When the pictures need to be charged, remember to be connected to WiFi and a charger.
Also try rebooting your phone, it clears up the cache memory and can also free up space.