The doc says wait until you feel better...

Do you feel better? If you and your therapist feel better about your chances, it is probable that the problem appeared to be muscular - as whiplash injuries often are - and you are on the mend. If so, a half-marathon should not be too much of a strain on a portion of your anatomy that will be well balanced, and not strained by the event unless you encounter tremendous headwinds. If you were on the other hand say, a mud wrestler... I'd say no.

The doc's concern is no doubt based on the possibility of vertebral damage, which would probably not respond well to impact exercise, and might not be feeling better so soon. The doc put the ball in your court, so be honest about how you feel and follow the sound advice you've been given. Exercise has circulatory benefits that should speed healing in cases of muscular injury, as long as the exercise does not strain the injured muscles further.