Brief Answer:
Depends on the cause.

Detailed Answer:
I read your question carefully and I understand your concern.

In order to give an informed answer to your problem it would be useful to know what is the cause of the blood vessel constriction. There are several possible causes like narrowing due to atherosclerotic disease, degenerative changes of the spine with compression of the neck vessels from bony or fibrous formations, trauma, vasculitis (inflammation of the vessels), dissection of the vessel wall etc. The first two are the most common causes which I'll address.

So some more data would be useful on:
-characteristics the of headache, other symptoms (vertigo/dizziness, visual disturbances, sudden falls, slurred speech, difficulty swallowing), evolution in time
-exams you have made which showed this narrowing of blood vessels
-other medical conditions you might have esp. high blood pressure, diabetes, high cholesterol, obesity, smoking, rheumatological problems.

If the cause is atherosclerotic disease management would consist in treating conditions which damage blood vessels like high blood pressure, diabetes, high cholesterol, stop smoking as well as blood thinners like Clopidogrel or combination of Aspirin/Dipyridamol with a statin drug like Atorvastatin. These measures serve more to stop the atherosclerotic narrowing though rather then reverse it. In severe cases surgical or endovascular intervention through a catheter could be considered.
Headache is not a common symptom of blood vessel narrowing unless there is a stroke though. Dizziness/vertigo, sudden falls etc are usually the case when there is narrowing with transitory lack of blood supply without an infarction (stroke).

If on the other hand headache is in the setting of degenerative spine disease appropriate treatment consists in pain killers like Ibuprofen and physical therapy.

I remain at your disposal for further questions, possible with the answers to the information I required above on history and tests you've had.

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