What type of doctor must I see to treat my headache?

PCP and Eye Doctor . A view of the optic nerve and retina can sometimes give clues to cause of headaches. At the very least it can rule out some problems such as brain swelling or vasculitis. Eyeglasses or prescription are rarely the problem. Ask your physician to consider an ophthalmology evaluation as part of your work up. Some neurologist and pcps can do that exam too with a handheld device.
See your doctor 1st. I'd suggest starting out by seeing your regular doctor, who can diagnose and treat most of the common headache causes. If your doctor is unable to find the cause, or if it's a cause best treated by a neurologist, your doctor can refer you to one.