It is going to come down to the underlying cause of the pain. A strained back muscle may need PT and other treatment to resolve. If it is resolved without any permanent consequence, you should be okay. (Disclosure: I am not a physician or health professional).
DoDMERB is focused on any current condition that does not qualify you for service. Even if you are DQ'd, each program (SA or ROTC or OCS) can evaluate you for a waiver.
Good luck to you.