Getting a message that says "iCloud storage is full" even though it clearly isn't?
Click the Apple menu and select log out. 
If a program is stuck and you can’t log out after saving work, the issue could be your machine was stuck. Reboot and watch the status after a restart. 
If your log out was clean then power off your Mac for 30 minutes. 


This lets whatever process runs on the server where Apple stores your documents to time out. Restart. Sometimes I’ve had to wait overnight with my iCloud off but usually this clears in time. Worst case, a call to Apple support would be needed if your other iCloud functions work and the Mac software is not hanging up. 

It is unlikely you need to check online, but your case looks to be a problem completing the upload, not no space in the cloud.