Getting a web page from another computer. How to do it better?

Question

Computer networks

Good afternoon! Such a problem. There are two computers on the network, both have access to the Internet, but one computer can only access 5 sites (not from the internal network, but regular sites such as mail, etc.), and the second computer has access to all sites. Both computers do not use a proxy, the DNS server on both computers is the same 8.8.8.8 (when accessing a banned site, I can easily get its IP, but when I try to connect to this IP, an unreachable error occurs), most likely, the blocking occurs at the router level (which I don't have access to). Please tell me the idea of ​​how to implement access to at least one site. I thought it was possible to somehow deploy a web server on a second computer, which would be an intermediary, so to speak, and on the first computer, in the host file, add a domain mapping to the IP of the second computer. Thereby,
Are there any better ideas than these crutches (other than contacting the admin)? External proxies are blocked.
The second computer is the office, my first laptop. The admin won't be back from vacation anytime soon.
Thank you!

Answer 1

"Both computers do not use a proxy"
So install any proxy on a computer with a full-fledged Internet
. And configure a limited computer to use this proxy.
Any googled proxy will do - ccproxy, wingate, the main thing is that it be free and downloaded from its home site, not a file cleaner