The Adobe Creative Cloud App should show Lightroom as up to date and version "CC (2015)". If not, perhaps you installed the stand-alone version of Lightroom? That can confuse the CC app. Almost anything can confuse the CC app. Whatever, you should be able to force the CC app to notice that Lightroom isn't up to date by removing Lightroom altogether, and then the CC app should show Lightroom as being available to install. You might have to exit and restart the CC app, and perhaps even reboot. Also, sometimes (I've found) it can take it a few hours to update itself with what is available. Goodness knows why. Removing LR shouldn't delete photos or catalogue, however, as always when messing with apps, make sure you have backups of photos and catalogue first.
My experience is all with PCs - no idea if there'a anything different for Macs.
Because you either aren't opening LR CC or you haven't actually downloaded and install the Adobe Creative Cloud Desktop app and then actually installed LR cc from that app.
You have to do both of those things to actually have Lightroom CC installed on your system.