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.
Having a chest infection can cause an array of painful symptoms that include chest pain, pressure in your chest, wheezing or shortness of breath and pain that intensifies after you cough. To help you treat your chest infection, you should consult with a physician to identify the cause.