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 do have a niggly cough which comes and goes. I am producing not what I would call phlem but white sticky stuff. I also have a pain at right lung and when pain is at its worst, it generates through to my back and up onto my shoulder blade. I do feel nausea also. The pain is there constantly.