While a rising heart rate will increase blood flow through the body, it does not necessarily correspond with an increase in the pressure of that blood flow. This is because blood vessels can increase in size (dilate) to facilitate larger quantities of blood. Even if your heart rate were to double, your normal blood pressure & high pulse may only slightly increase blood pressure.
Beta-blockers cause the heart to slow down and so some of their side effects can be traced to that mechanism of action. Dizziness, weakness, fatigue, and fainting are possible. Beta-blockers also affect the respiratory system, so other side effects include shortness of breath, difficulty breathing, and chest pain. Beta-blockers should not be withdrawn suddenly, as that could result in a heart attack or sudden death.
Headaches strike over 90% of adults each year. You may be able to wait out some and let them pass, but others may be a sign that your body is asking you to take action. There is a chance that your headache could be a symptom of high blood pressure. If there are no other causes of your headache, you should ask your healthcare provider about getting your blood pressure checked.