I have had whiplash from a car accident, and my doctor sent me for physical therapy within a very short time after the accident (like, less than 3 days). It makes a difference because even if you are doing exercises (which at that point are just simple movements) when you still hurt from the trauma, they keep things from stiffening up and suddenly being unusable after 6 weeks. See your regular doctor and ask for a referral.
I agree that your primary is a great place to start. I've also had whiplash and it can feel like something you can deal with early on, those injuries can linger for years. Maybe even forever. Soft tissue injuries are problematic. It definitely can last and a neck injury can come back to haunt you. It becomes 'that place' where you flare with pain every time you are tense. Physical therapy is definitely something I'd consider. Chiropractor can be helpful. They often do prescribe muscle relaxers for discomfort right after the accident. An ER could do that or an urgent care if you say docs are currently unavailable. But I'd consider taking care of this as a preventative step. I had an accident years ago that I feel the ramifications for frequently in headaches and stiffness in that area. Wish I'd done more when it happened but it is easy to blow off. Don't blow it off.
Hello~I would certainly see your GP, you don't want any of your symptoms to get worse.
As to a chiropractor, I see one and he helps immensely. He has taken x-rays and looked at them and definitely adjusted differently after seeing what areas need the most attention. I guess all are different however, but all of mine have been good and used the x-rays to a good advantage.
I hope you feel better soon. Whiplashes are no fun.