I can't help, only commiserate.
The updates to CC to accommodate LR6 licensing seem to have made it rather unreliable. This morning I could run CC app and it thought I was signed in to Adobe. LR CC would run, and it thought I was signed in to Adobe. But Photoshop wouldn't run, insisting that I sign in. When I tried to sign in, it said I was already signed in on 2 other machines (not correct), and refused to continue. Signing out in the CC app and rebooting eventually made it behave.
Have you tried reinstalling the CC app?
Could this be related to the fact that I have the CC logged in on my Mac Book Pro even though it is not being used. Do I need to actually log out from one computer before log on to the other.
You should be able to sign in to your account on two computers at the same time. It's always worked for me that way before, but not today.
I just think Adobe is monitoring compliance via the Creative Cloud Manager more closely. Two installations with only one in use at any point in time.
Yes, but on this occasion the other machine on which I have CC apps was switched off!
Did you get your problem sorted out? If not, I've found the chat support helpful if time consuming.
When CC authentication works, it's fine, when it doesn't it can be very frustrating, and installing and managing CC accounts is not intuitive. Just look at all the problems people have raised on this forum. They can't all be stupid. I reckon authentication-related problems have cost me about 2 days of my time.
Authentication of user licences is Adobe's problem, I resent it when it becomes mine.