> the [office computers] prevent software installation, so I would need to manually type from a manager synced on my cell.
I don't know about other Password Managers, but LastPass lets you access your vault using any web browser. So long as your network doesn't block the LP site, you can access your password manager from anywhere.
On a similar note, Keepass can be used without admin rights with the portable version, so you can keep the portable executable along with the encrypted db file in some secure and accessible email account/web service that your network doesn't block.
I don't know about other Password Managers, but LastPass lets you access your vault using any web browser. So long as your network doesn't block the LP site, you can access your password manager from anywhere.