Okey dokey:
The headache is due to a rapid change in blood pressure initiated by the cough sequece. When a person coughs hard the vagus nerve is activated. This causes the heart to change rate. It is nothing to be worried about.
One problem is that continual coughing inflames the surface of the trachea and makes it more susceptable to infection.
Without you having seen an M.D. it is inappropriate for me to suggest medications, however if I felt sure you didn't have a serious problem, I would purchase an over-the country cough suppressant, of which there are several.
Usually these problems are self limiting, and once the cough is suppressed for 72 hours it does not come back.
Don't hesitate to see your M.D.
amber try buying a humidifier because your dry cough is related to your environment. Its the machine that shoots out cool mist. Sleep with it on every night, where you live might have dust, pollen, or what ever else but Doctors say this can be on every night, it moisitens your lungs after that you will be fine,