Given the symptoms you provided (faint episodes, “pounding heart”), you might be experiencing not absolute, but relative hypotension due to the recent start of antihypertensive therapy. Your organism might take up to two weeks to adapt to the lowered blood pressure. Meanwhile, the organism might recognize this new situation as hypotension even the actual blood pressure is still above normal values, thus falsely causing certain of the hypotension symptoms, such as: dizziness, nearly fainting, as well as tachycardia. The heart causes tachycardia because it tries to compensate for the decreased blood flow due to the hypotension.