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Sudden onset headache which is throbbing type may occur due to migraine, but there are associated features as nausea, vomiting, blurred vision
etc. You have pain with exertion mainly on climbing up stairs, or on coughing so it should be evaluated in detail also. I would advise you to get your ENT check up done to rule out any problem of sinusitis
, and also EYE checkup for any refractive errors. If everything come normal you can visit a Psychiatrist
for expert opinion for pain. Migraine or Tension type headache are other possibilities.