Hello Instinct,
Yes, birth control pills have a listed side effect of high blood pressure. You should definitely discuss with your doctor (eitheryour OB/GYN or the Dr. that perscribes you pills) the symptoms you are experience.
I am not, though, convinced what you are experiencing is due to high blood pressure. Have you taken BP readings with a cuff, or are you assuming that you sided throbbing headaches are caused high blood pressure. There are a number of different conditions that could be causing your symptoms! One they might one to consider is something called menstrual migrane, which is caused by fluctuating hormone levels associated with menstruation. The symptoms of this condition are similar to what it seems your are describing.
Like I said, absolutely make an appointment with your doctor to discuss your headaches and your birth control medications!
To your health,
Neil MD