you just need to sign out from your work computer to preserve your two concurrent sign-ins. and if you do forget to sign out from the work computer, that's not a problem either because if you start to sign in to a 3rd computer, you will be offered the option of which of the other two computers to sign out from.
more info:
you can install the cc desktop app from here https://creative.adobe.com/products/creative-cloud on as many (mac and/or win) computers as you own and use it to install all (or some, if you want) of your cc subscription programs.
the only (insignificant for internet connected computers) limitation is that you can sign-in (and therefore start your adobe programs) on, at most, two computers at any one time. because you can sign out from either (or both) signed-in computers using a 3rd computer, this could not (imo) be easier. https://helpx.adobe.com/download-install/using/install-apps-number-of-computers.html