I second and third the advice from above, and want to caution you about what BP meds do and how they do it. High blood pressure results when arteries/arterioles remain constricted, affecting pressure the way pinching a water hose builds pressure. There are times when this is useful, such as when rising from a chair. Most of the time, it endangers the brain and vital organs when the pressure is high and unrelenting. BP meds work via various means to inhibit the tightening (vasoconstriction) of these blood vessels, and/or to relax the tiny muscles that line them and make vasoconstriction possible. The effect is vasodilation, or relaxation of the arterial walls. Of course, this can provoke dizziness when rising from a chair under the influence of these meds. Apparently, it affects other forms of exertion, such as your exercise. I'm sorry you've been forced to make this choice, but it may be a temporary one.
As you've probably been told, exercise has a tonic effect on high blood pressure. Don't expect it to be immediate, and if done in conjunction with these meds, I would not expect to start out winning the local 5k. If you can hang on through the annoying symptoms, with appropriate adjustments made by your doctor, the effects of the exercise may eventually pay off, at least enough to reduce your prescribed dosage and get your life back. By life, I mean more than what you are used to. If you've been on antidepressants, you may know that some studies indicate a greater effect of exercise on mood than medications alone can produce. All in all, you may be in better shape to enjoy running going forward, than fellow runners with serious injuries. Now, that can be depressing!