I had the same problem, I fixed it by completely removing CCC and reinstalling afterwards, it seems like updating the drivers doesn't work poperly.
This is really what you should do with every GPU driver update--scrub out the old, reboot, install the new. That's what I do every upgrade. It's a pain in the behind and takes a while, but it saves a whole lot of trouble in long run.
Speaking of, I just did all that earlier

to upgrade from 12.1 to 12.3. Booted up Skyrim after it patched and jogged from Rorikstead to Whiterun. No gray pixel squares, no wacky shadows, and no perceptible performance decrease (or increase, but my performance was awesome before, so) from 12.1. I'll go ahead and give these new drivers a thumbs up.