If the symptoms are occurring after exercise, the most common cause would be a sudden drop in blood pressure. Normally when one does upright exercising there is a rise in systolic blood pressure (the upper number) and a slight fall in the diastolic blood pressure (lower number). The systolic blood pressure should slowly drop back to normal during an active cool down period. If one sits rather than actively cools down, the blood will be pooled in the periphery unable to reach the brain. The blood pressure will drop precipitously. The lack of blood supply to the brain can result in dizziness, nausea and even passing out. Some people are more sensitive and have a larger drop. While most people don't pass out after an injection, sensitive individuals can.
The normal drop in blood pressure can be made worse by certain medications (especially blood pressure medications). Inadequate hydration prior to exercise will worsen the problem.
Inadequate nutrition prior to exercise can result in a low blood sugar which can cause dizziness.
Hydration, adequate nutrition, and an active cool down period may be helpful in these situations.
Unfortunately there are less common causes which can be lethal.
If the systolic blood pressure does not rise with exercise, there will be dizziness and possibly a loss of consciousness. Sudden death can occur. The blood pressure does not rise when blood is prevented from exiting the heart. The most common conditions causing a blockage are aortic stenosis and hypertrophic cardiomyopathy. Hypertrophic cardiomyopathy is the most common cause of sudden death in young athletes.
With coronary artery disease, the diastolic pressure may actually rise rather than fall. Blood pressure is always checked during a cardiac stress test. Chest pain and shortness of breath are not always present in coronary artery disease. Weakness or dizziness can be the only symptoms.
There are also abnormalities of the heart rhythm which can occur with exercise. These can have similar symptoms and also cause sudden death.
There other serious medical problems that can cause similar symptoms.
Anyone with these symptoms should have a thorough physical by a physician to rule out a serious medical problem. Do not assume the symptoms are benign!