How to build a network packet filtering system ?

As mentioned in the title,

I proposed to develop a packet filtering system for a computer lab,

for eg, there are 20 pc, 19 students and 1 tutor

and the system will allow the tutor pc to control the network access of the 19 student pc,

where allow or not allow to access the internet only.

is it possible to do it by c# programming language? or i shall do with Java, C or C++?

Please advice.

ThANKS.