Why did Arwen go to find the hobbits?

[Meneltarmacil]

The absence of Gildor really wouldn't affect Elrond's sending a messenger to search for Frodo. Aragorn had already gone to wait for the hobbits at Bree, and had probably told Elrond when he'd have brought them to Rivendell. Upon learning that Aragorn had not arrived back on time and that the Nine were abroad, Elrond sent his messenger (in this case, Arwen) to search for Aragorn and the hobbits.

As far as how Elrond wouldn't know that the ringwraiths were searching for the hobbits while Aragorn did know about them, I would guess that in the movie Aragorn didn't find out about the ringwraiths until after he was on his way to Bree.