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.
Sinus drainage in the throat, or post-nasal drip, is the sensation of mucus in the back of your throat that triggers an urge to cough or swallow. While the condition itself is a symptom and not of serious medical concern, post-nasal drip may lead to throat irritation, night coughing and difficulty sleeping.