Yep, neurologist is a good place to start, especially with neck problems.

In general, you can see a chiropractor for neck problems. I don't know if many insurances cover it, but our family friend is a chiropractor and he's helped my back and neck problems a lot. They can even help with neck and back injuries in particular. My mom met him when she had slipped discs in her back.

Obviously I don't know your specific situation, but just pointing out that a chiropractor may be an option in case a doctor wants surgery