Exercise can be a trigger of migraine which will cause headache and nausea. Exercise can also trigger electrolyte imbalance, dehydration, spinal problems etc all of which can cause headache and nausea. Your son’s blood pressure too can shoot up with exercise and cause these symptoms.
Post exercise nausea or exercise induced nausea is usually due to over exercising, or abruptly stopping exercise, or over hydration. Drinking too much water before, during or after exercise could also be the cause. Let him eat some salty snacks before exercise and see if it helps. Exercising on empty stomach which causes blood glucose to dip with exercise can also be the cause. One should exercise after 2 hours of a light meal.
Exercise intolerance is generally due to heart conditions such as aortic valve insufficiency and cardiac arrhythmia. Go for a holter test and see. Resting EKG may be normal. Also a heart ECHO will need to be done. COPD or chronic obstructive lung disease is another cause and pulmonary function tests should be done. Chronic fatigue syndrome, anemia, obesity, thyroid problems and diabetes are the other possibilities.
Since I cannot examine your son and know other related conditions he may be having, nor is a detailed history possible on net, I have listed the various possibilities that should be looked into. Please consult your PCP for primary examination followed by proper referral. Take care!