What I'm looking for is a solution where I can go to tunnel.example.com, login, and browse any website through that portal, without the need for a systemwide VPN or SSH tunnel, which isn't possible due to a school or work controlled computer (on which I have no admin access).

I would prefer to host the portal on my own website, and run it through a VPN configuration I already own (NordVPN or PIA).

Thanks, Seb