First of all, keep in mind that I am unable to diagnose you because I am unable to examine you, this forum is for educational purposes.
The symptoms you describe are consistent with cervicogenic migraine headaches/dizziness (Headaches/dizziness that comes from the neck). This often occurs after a neck insult of some kind such as trauma (car wreck), or an episode of inner ear infection (viral, etc) that damages the vestibular system and leads to neck misalignment. Neck problems then lead to dizziness and headaches. Medications such as elavil (amitriptyline) are very effective at preventing migraine headaches, and would be expected to provide some benefit for you. It is true that inexpert neck massage will exacerbate your symptoms,but a skilled physical therapist that has experience in treating cervicogenic migraines would be very helpful for you. I would also suggest you take a muscle relaxant, such as zanaflex to assist with the physical therapy. Alternatively, some people have "basilar migraines" that do not specifically involve the neck, but get better with preventative medications alone (elavil, topamax, nadolol, etc). When you see your neurologist, they may be able to inject trigger points in your neck that are causing discomfort. Many cervicogenic migraine patients expierence significant temporary relief with Botox injections into their neck muscles. I would also suggest an MRI of the Brain and Cervical spine with contrast to rule out any structural pathology.
I hope this has been helpful.