I would guess its an ovarian cyst. I have pcos and have had many. They can give you Bcp to shrink it. I've had to have 2 surgically removed over a 10 year span but they were large. A simple ultrasound can detect a cyst. They can cause changes in your period and can prevent them as well.
I would go see someone about i first thing tomorrow, Monday unless the pain is unbearable. The regular doctor will need to refer you to a gynecologist.
There are a few reasons below; my personal opinion is that it is your ovaries causing the pain. The way you describe one side then the other seems to fit. Ovaries at your age can get benign cysts which cause pain. It could be late ovulation, but then it would be more like cramping then pain.
If the doctor says to wait until your next period before a referral to a gynecologist, i would insist that you really need to see one as the pain is terrible and unlike regular menstrual pain.
Here's an explanation of sore ovaries with some natural treatment ideas. I have tried Black Cohosh and it works well.
http://herbs.lovetoknow.com/Herbs_for_Sore_Ovaries
Take care and try a hot pack on your abdomen, it will help, too.
http://www.livestrong.com/article/141297-causes-cramping-no-period-not-pregnant/
and
Late Ovulation
In most cases, menstrual periods start 12 to 16 days after ovulation, or release of an egg from the ovary, the APA reports. Cramping may signal the start of a normal period. If a woman ovulates later than normal, abdominal cramping after she expects her period to start may mean nothing more than the occurrence of an extra long menstrual cycle. If the uterine lining builds up thicker than usual due to a longer-than-normal cycle, cramping may be more severe than normal.
Read more: http://www.livestrong.com/article/103515-causes-abdominal-cramping-period/#ixzz20gROe9mb
And now the throbbing has started on the right two. It doesn't feel like cramps I've ever had before.