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.
Diaphragm pain: Irritation of the diaphragm from abdominal or chest can be referred toor felt in the shoulder. That is the muscle that expands the chest when you breathe. Coughing can be due to allergies, some medications, reflux, viral or bacterial illness among other things. I hope. ...Read more.