While I'm not a big fan of chiropractic, this modality of therapy can be useful in cases like yours.
Most who have visited a chiropractor have had bad experiences to relate. I'm speaking of chiropractors who pull muscles while trying to "adjust" the spine.
It is very important that a chiropractor work slowly to release inflammed soft tissue before attempting any abrupt adjustment of the neck or spine.
If your doctor recommends this chiropractor, then I would imagine they have worked together before. Mixing allopathic medicine, for instance, strong anti-inflammatory or pain medication with chiropractic would yield the best results.
Remember, you are in control so advise your chiropractor of your comfort level. If you feel a sharp pain after an adjustment, let them know.
As far as permanent damage, there's little risk of this, since you've already had a full medical workup, have no broken bones, ruptured discs, or other conditions where a chiropractor may exacerbate a spinal problem.