How can I host a proxy server on my own computer, for use on a different computer?

[cubex_de]

I've seen lots of people ask similar questions, but not this one:

I want to host my own proxy server for my own private use without buying a host, simply by setting up a no-ip.org account to redirect to proxy software on my own computer. Then I want to access this proxy address from a different computer. I've already used no-ip.org to set up a uTorrent web UI, my router's remote access, and the Media Player Classic web UI. I DO NOT want to use a proxy on the same computer the proxy is running on, such as Tor or Privoxy.

I am actually trying to use this so that while at work I can pull up sites like YouTube and Gmail without them being blocked, and I do not want to have to rely on getting new public proxies all the time. I want my own private proxy I can use.

Please let me know if there is a way to do this and what I need to do it.
I am not worried about my ISP discovering my proxy, and my filter at work is all done by domain and not IP, which means I can unblock it on a daily basis. Please do not tell me all the ways that this won't work, only how I can make it work.