Yes there is an extension for the Google Chrome web browser that will allow you to do this. It is called Chrome Remote Desktop. You can install the extension from the Chrome Webstore.
It will allow you to remotely access another computer through Chrome browser or a Chromebook. Computers can be made available on an short-term basis for scenarios such as ad hoc remote support, or on a more long-term basis for remote access to your applications and files. All connections are fully secured.
Chrome Remote Desktop is fully cross-platform. Provide remote assistance to Windows, Mac and Linux users, or access your Windows (XP and above) and Mac (OS X 10.6 and above) desktops at any time, all from the Chrome browser on virtually any device, including Chromebooks.
Updated: If your school does not use the Google Chrome web browser, the easiest way is to install a portable version of Google Chrome on a USB Stick at home
Then install the Chrome Remote Desktop Extension to the portable version