I think you're a bit confused. iCloud Storage does NOT give you more space on your iPhone. And iCloud Storage simply gives you more space to sync data with iCloud, NOT move data off your phone to iCloud. Once purchased, your iPhone storage can't be increased. iCloud is a syncing service, NOT an archive. You really only need to buy additional iCloud storage when you get to the point you have exceeded the free 5GB of iCloud storage, which would prevent you from backing up your iPhone. If you are using less than 5GB of storage in the cloud, buying more iCloud storage really didn't help you.
If your iPhone doesn't have enough space, the next time you buy an iPhone, you should buy one with more memory.
The advice from SravanKrA is great to help you learn how to clear storage on your iPhone.