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.
I have had this cough for 4 months now. The dr has changed my diagnosis everytime I go (which is frequent). The cough starts with a tickle in my throat, which makes me cough this loud obnoxious cough that feels and sounds dry but produces this sometimes thin, sometimes thick white/clear mucus. This happens all the time, day night whatever.