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.
The sharp pain in chest, when the person coughs can be due to several reasons . If the person is a chain smoker then it could be some major problem . It could be due to chest infection , muscular cramp or any heart related problem also . To know the exact reason, better to get examined by the doctor.