> "look it up" and "search for it" somehow became "search it up" with the young people

It wouldn't actually be necessary for the phrase "look it up" to exist for this to happen. You're free to apply the particle "up" to pretty much any English verb if you want the semantics that it provides. Compare rustle up, turn up, etc.

You might also want to take note of the episode of Kim Possible where Ron is unsatisfied with the performance of an actor studying to play him, and tells the actor to "Ron it up".