The most tried and true natural alternative is losing weight. How are you in this department? On your vegan diet you should be getting really slender.
Beyond that, I do believe it's a chemical thing that your body is producing or not producing that leads to your blood vessels getting constricted. It's very likely genetic. Didn't your doc ask if your parents had the same problems?
BTW, do you take your BP reading at home? Is it still high? Mine is perfectly normal at home but crazy at the doctor's office. If this is the case, you can ask for a 24-hour monitor then you'll see how you are when you are away from the doc's, and yet it will be an official reading.