I am very not sure what you're trying to say. You say it saves the photo, but I don't understand the problem.
For anything storage-related, go to Settings > General > Storage & iCloud Usage and check your iCloud storage usage there. There is no charge for the base 5 GB, and you can do whatever you like with it — even back up your phone to it, as long as it doesn't exceed the 5 GB limit. ICloud only backs up the most important things on your device, so it's more than likely that there will be enough room.
Also, just above that, you'll see how much free space is available on your device. If you have gotten the popup that says there isn't enough space to save a photo or video, you can see what is hogging the most space on your phone under Manage Storage on that same screen.