I am wondering if there is a way that I can send myself an X prompt over SSH from my house to my work computer.

i.e. I use linux at work. I want to be able to ssh to my home computer, make it send me an Xshell over the current SSH connection to my computer at work with "startx -display xx.xx.xx.xx:0:0 .

I have looked into SSH tunneling and Xforwarding, but I'm not sure this will let me bypass my work's firewall. I can't just send it to the IP of my work because obviously the router won't forward it.

Please advise.

You can use X forwarding by specifying a flag in the ssh command: "ssh -Y ..." or "ssh -X ...". All traffic is forwarded through the SSH connection, so if you can use SSH now then you can use X forwarding. X forwarding will allow you to start individual X apps from the prompt, but not the whole desktop environment. Also X forwarding is somewhat slow over the Internet.

If you want to get a remote desktop type of thing, you can use VNC. Most Linux distributions come with RealVNC and/or TightVNC, etc. Set up the VNC server on your home computer, and use a VNC client to connect to it.