Pretty much this. You need to use a proxy server that's outside of Pakistan (or any country that blocks Youtube) simply Bing proxy server and you should have a list of servers available to you with instructions on how to use them.
There's a lot of workarounds for it. You can either download a VPN app like Tunnelbear but they usually have a data limit.
Or you can run a Google search for free VPN servers and copy/paste their settings manually into the Windows phone 8.1 VPN settings. There's a guide with screenshots here if you need any help with that : How To Setup VPN on Windows Phone 8.1 In Minutes
Agreed vpn is the easiest way. Yes, you need to pay, but it is worth it.
Windows phone doesn't support Openvpn, so the best services are not supported on the phone, though they are on the pc, obviously; but most services have options that would be compatible with the phone, as well as better security for the pc. Most services allow you to connect multiple devices. Good luck.