You lunge out and grab the branch. You spin around to find the zombie just outside arms reach. You haul back with the branch and swing for the head. The branch connects solidly and the head pops like a grape with a sickening pop. After passing through the head, the branch connects with small tree just behind him and shatters with a night shattering crack.
There is an uneasy silence for a few moments, followed by the sound of frantic movement from every direction. You don't have the strength to fight them all. You survey the area.
There's a tree that looks reasonable easy to climb nearby. Maybe you could hide up there. You could also hide under the body and hope for the best.