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.
A cough can be the result of a respiratory tract infection such as the common cold, acute bronchitis, pneumonia, pertussis, or tuberculosis. In the vast majority of cases, acute coughs, i.e. coughs shorter than 3 weeks, are due to the common cold. In people with a normal chest X-ray, tuberculosis is a rare finding. Pertussis is increasingly being recognised as a cause of troublesome coughing in adults. After a respiratory tract infection has cleared, the person may be left with a postinfectious cough. This typically is a dry, non-productive cough that produces no phlegm. Symptoms may include a tightness in the chest, and a tickle in the throat. This cough may often persist for weeks after an illness. The cause of the cough may be inflammation similar to that observed in repetitive stress disorders such as carpal tunnel syndrome.