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.
Postnasal drip creates an annoying feeling that makes you want to constantly clear your throat. Because the feeling of the liquid in your throat is irritating and contains inflammatory substances, postnasal drip also can trigger a cough, which often gets worse at night. In fact, postnasal drip is the most common cause of chronic cough. Excess mucus running down your throat may also make you feel hoarse and give you a sore throat. If the mucus plugs up the Eustachian tube -- the tube that connects the throat to the middle ear -- it can lead to a painful ear infection. When mucus blocks the sinus passages, it can lead to a sinus infection.