Do you need an ankle brace for a third degree ankle sprange?

yes, yes, and absolutely! a third degree sprain means you completely ruptured the ligamentous tissues of the joint (i.e. a complete tear). once the integrity of the ligaments have been compromised the joint loses its containment.
from a healing perspective: ligaments do not have their own blood supply thus they take quite a while to heal. if the two ends of the ruptured ligament are not in close proximity to each other they might not ever heal back together or at best, heal together so loosely that they provide no tension to contain the joint. the looser the ligament heals, the higher the re-occurrence of the mechanism of injury (i.e. twisted ankle or whatever happened that gave you the sprain in the first place).
wearing an ankle brace puts the structures of the ankle in a more compact "close-packed" position, which allows for more efficient healing. moreover, the brace will provide support to the joint that was lost when the ligament ruptured.
hope this helps and makes sense to you.