The DoDMERB physical examination is good for all service academies and ROTC programs. As your son applies to the different service academies and ROTC programs, they will all add his name to the DoDMERB system at different times. So it is possible that you will get multiple letters for each program that he applies to. The physical exam is also valid for 2 years from the date of the exam.
Your son needs to contact the contractor to schedule the physical exam within 5 days, the actual examination will not be for at least 2-3 weeks, and same with the eye exam. If there are issues that preclude his from getting the exam right away, I would contact the contractor and let them know. They may be able to work something out for you, and if not contact DoDMERB and they will definately help.