If you are unable to install programs on a computer, you may still be able to use Zotero by a portable version of the program from an external drive (e.g., a USB drive).

A community-developed portable version of Zotero is available from here. Note that this portable app is not officially distributed by Zotero, and the Zotero developers can provide only limited support for it.

Additional discussion of the portable Zotero 5.0 app is available here.