Complicated, telling the truth is best.
BUT don't offer any extra information than what is asked about this accident and your injury from it..
(your past mental/physical history is not relevant)

If you went to your own dr about this new injury, your dr should be able to write a letter about current condition and findings..

But they probably should have sent you to PT for evaluation & possible treatment of your neck...
Soft tissue injuries , trigger points , spasmed muscles can cause symptoms that can be resolved with proper treatment.