Final answer:
The switching center where nerve fibers from the ears cross over to carry messages to the higher centers of the brain is the medulla oblongata. It is part of the brain stem and controls vital functions like breathing and heart rate.
Step-by-step explanation:
The switching center where nerve fibers from the ears cross over to carry messages to the higher centers of the brain is the medulla oblongata (option A). The medulla oblongata is part of the brain stem and is responsible for transmitting sensory information from the ears to the higher brain centers. It also controls vital functions like breathing and heart rate.