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Some of the headache and neck stiffness can be normal with constant coughing; however; you need to monitor your symptoms, at its worse, this can represent meningitis which needs urgent evaluation.
Monitor your temperature for any fevers, also see if you have any back pain if you were to lay flat on your back and raise either legs straight into the air - pain with this maneuver or fevers can indicate possible meningitis and you will need more evaluations to rule it out.
I wish you a speedy recovery,
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