Blast Exposure and Brain Injury Prevention Act This bill requires the Department of Defense (DOD) to submit to Congress a report setting forth: (1) a plan for the Defense Health Agency to accelerate cooperative research and development on therapies for traumatic brain injury and post-traumatic stress disorder; and (2) recommendations for legislative or administrative actions to carry out the plan. The bill requires military departments to include in the military service records of members of the Armed Forces documentation of information on any blasts to which such members were exposed during service in the Armed Forces (whether in combat or training). DOD shall: (1) review the firing limits for heavy weapons during training exercises, and (2) establish a research and development program to improve the efficacy of personal protective equipment to reduce blast pressure or protect against brain injury from exposure to blast pressure waves.