Internet connection sharing over wifi

I have just bought a laptop in addition to my desktop PC, and am looking to connect both of them to the internet in my room at university. Unfortunately there is only one ethernet socket in my room and IT regulations only allow one registered computer per student.

Would it work if I connected the desktop via ethernet as usual, then used internet connection sharing over wireless to connect the laptop to the internet ( I would try this myself but that would require buying a wireless adapter).

Alternatively could I get a network hub and put it between the two computers and share the internet from the desktop over that? I can't put a router connected to the wall socket as that's against IT rules there.

Thanks if anyone can lend some advice, and if you have any suggestions on hardware to get, please say! (cheap is good, as long as it's going to work!)