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.
The discharge may also bypass your nose and drain down the back of your throat. You may feel a tickle, an itch, or even a sore throat. This is called postnasal drip and it may cause you to cough at night when youâre lying down to sleep, and in the morning after getting up. It may also cause your voice to sound hoarse.