Chemistry - How to determine oxidising and reducing agents in the reaction between ammonia and hypochlorous acid?

You're on the right track with assigning oxidation numbers to each element. And you've assigned them successfully.

To successfully complete the task you need to define a few terms:

What's oxidation?

What's reduction?

What's the oxidizing agent? Try thinking of this in terms of what oxidation is, and then try figuring out what an oxidizing agent would do.

What's the reducing agent?