New
#11
Ya, don't worry about anything! Be glad that you have one of the best operating systems out there! =)
The updates install themselves in the background without you knowing, so yes, it is very likely that the update has installed itself (yet still needs to restart your computer and load up to finish up completely).
Don't stress yourself out about a thing!
(Shutting down the computer is still okay, once it gets started up, it will continue. Yet restarting it would be more preferred in general)