When you do downward facing dog (or any pose where your head is below my heart), what happens is the blood is rushed towards your head, that is probably causing you dizzy and nauseated.
The posture no doubt helps in flexibility by stretching the hamstrings and calves and on the other hand strengthening the arms, legs and back. But, if you have high blood pressure, you should be careful while doing this posture, rather you should avoid this posture and any other postures that are more or less inverted ones where position of the head comes below the heart that brings more blood flow to the brain. And if you feel dizziness /nauseated, you immediately stop the posture and come back immediately and relax in balasana (child's pose) to normalize yourself. You may also try to rest your head on pillows.
This posture should not be done if you have detached retina or dental bone grafts, where you should not allow your head to be below the level of your heart, just like High Blood Pressure.
It is better you should go for dietary lifestyle modifications to alleviate High Blood Pressure.
