Have you had any physical therapy for the neck at all?
If you prefer to avoid chiro again try PT. A good one of course..

The neurologist did not mention PT or anything? hmmm.
If any dr is not being of much help seek out a better one..or get another opinion or more.
It's your life so you have to be proactive to find the best care possible, don't settle for less.

PT often can help with whiplash/soft tissue injuries..