The instructor should not assign you a project using specific hardware that cannot complete the project.
I don't see anywhere in the assignment, other than OP's interpretation, that UDP is a requirement.
OP, how would you set up a client and server to exchange data using just two PCs? The same logic applies when one or both of the computers is an Arduino. One of them needs to be a client, and one needs to be a server. One needs to supply data, and one needs to request it.