It could be said that mathematics is the language of physics. That is another way of better understanding what is physics. Numerical values, units of measurement, and similar concepts are all mathematical in nature, and are used to describe physical quantities in the most accurate and precise manner.
In brief: Cough headache. There are a couple of possibilities. Coughing can raise the pressure inside your head, which can cause pain sometimes. There is also a poorly-understood entity called the primary cough headache,  that is associated with coughing, straining, laughing, crying, etc.
If your body is low in iron, swelling and irritation in the back of your throat could be a symptom, which can lead to coughing. If this sounds familiar, then an iron supplement may be all you need. Check your drugs: Meds, like ACE inhibitors prescribed for high blood pressure, can create the side effect of a dry cough.