I work at home, and have a desktop computer that is pretty locked down, sometimes I really just want to use my laptop to do my work, but since its a personal device I can't login to my stuff. The desktop can't have anything additional installed on it. So is there a way to stream HDMI out to view on a chromebook (pixelbook) and then I could use a wireless usb mouse and keyboard.
Not really sure what you are looking to do, you can't use a laptop as a screen for a computer, the video connections are outputs only. If the desktop won't allow you to connect a wireless dongle and install it, contact your work IT department, they should be able to connect to your system as an admin account to allow it to run the setup.
What you may be able to do is use a remote connection to the desktop from a laptop but that requires remote access rights on the desktop which you are not likely to have.