The blogs authentication is currently tied to the LAs instance. That means if you need access to a glow only or private blog in another Local Authority you will need the tile for that instance on your Unify Launchpad. Your school Unify administrator will be able to make that Tile available for you to your personal launch pad.
Here is a quick guide to Activating a Glow Blogs tile (pdf) for Unify Admins.