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The body’s normal response to low blood pressure is an increased pulse rate.  The problem you are describing may be due to the fact that many of the medications for blood pressure can cause both a lower pressure and a decrease in the heart rate.  It sounds like your pressure may be slightly low and the fact that your pulse can not respond to take up the slack results in the feelings of dizziness, headaches or nausea.  Talk these symptoms over with your doctor, as you may need a decrease in the dosage of you blood pressure medication.