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.
Cough. As the discharge from your sinuses drains down the back of your throat, it can cause plenty of irritation, especially over a long period of time. This can lead to a persistent and annoying cough. A sinus cough is particularly aggravating because it tends to be worse at night, making sleeping difficult.