You only get one back and neck so even though you are under the care of a military doctor, you need to take matters into your own hands and seek medical attention out side of there. If you wait too long, you could do damage to your nerves. That is the big thing, the nerves. If you wait for referrals or for a military doctor to decide that you need an MRI, you may damage your nerves. See if he will at least order an EMG. Do you have spasms?
Right now you may be sore and the pain may go away but you don't want to wake up one morning, long after your service related insurance is gone and find that the accident caused damage to your neck. I would insist