That puff of air at the eye has nothing to do with brain injuries. It is to test intraocular pressure for glaucoma. Some optos use an anesthetic and a device that touches the eye to measure pressure.

VEMPS and Caloric tests are for inner ear/vestibular issues, not sensory processing like a VEP or AEP.

VEP and AEP testing can be stressful because of the processing load it causes. But, that stress should resolve in a day.