Good luck with that. FiOS costs a heap amount of money. What I'm guessing your school can't afford. Luke, just drop it, and don't watch youtube in school.
The speed mainly depends on the service provided to you. Reduce the number of system that share the resource. This will automatically increase the speed. As number connections increase with a single resource the speed will decrease.
Okay well unfortunately the admins won't ban youtube due to it being an educational resource so I am stuck with this then. However I have a theory and will this work:
What about splitting the schools internet into parts that all link up to our main server? So multiple internet connections. That would ease the work load and split loading times in half. In theory. Will this work?
But no, it won't really help much, as all the traffic is still on a single connection going in/out. There would need to either be multiple pipes coming in, or at least a fiber line. And since neither of these are within budget... I'd have to say your'e S.O.L.