My BP has started to go up in the last few weeks. Diet has not changed. Doctor is putting me on a water pill. My questions are would an increase in workout intensity or a lack of a certain vitamin or mineral cause this?

Attached is a link from the American Heart Association for more information. There is a section that talks about your risk of developing hypertension, which may in part answer your questions.

http://www.heart.org/HEARTORG/Conditions/HighBloodPressure/High-Blood-Pressure-or-Hypertension_UCM_002020_SubHomePage.jsp

If your Blood pressure is increasing then you should become aware of the reasons as to why it is happening.Bringing lifestyle changes into your daily routine is something you should be looking into.Exercising or staying physically active,eating less of salt and following your doctor's advice is something which is going to help in the long run.