I would strongly advise you to see the doctor first before you see any chiropractor or osteopath, or anybody else at all for that matter. Don't mess up with neck pains until its clearly established you don't have a trapped nerve or a whiplash problem.
Once that is clear then go for it, chinese massage, chiropractors, osteopaths, accupuncture, anything works fine.
I suspect that you have strained one of your muscles, the one that goes down from the neck down to your shoulder blade, its a very thin muscle but affects the head because its attached to the back of the head. They are two small muscles running down from the back of the head individually to the shoulder blades. Those are the muscles that helps us to keep the head straight or lift it up, or else our head would fall down, (chin down touching the chest) like a lifeless dummy if you can imagine what I am trying to imply.
When these muscles suffer any strain or injury, or sometimes even just continuous wrong use of this muscle like watching TV while in bed with lots of pillows which forces us to maintain the head in a position to watch tv, these muscles start getting strained and then subsequent result is headaches on parts of the head, sometimes just on one side.
So I would strongly advise first to have it looked by a doctor, just to eliminate any other problem, and then carry on with other treatment.