Is this normal?

During my period, I sometimes experience cramps that keep me immobile for at least a day or two, and I often throw up. Is this normal, or should I be worried?

I'm sixteen and have been getting my period for 5 years now and it didn't start until 2 years ago. I only throw up sometimes, but the cramps are always unbearable. My period is never on time (it's always either a week early or a week late) and the amount of days always changes (anywhere from 3 to 9 days long.) None of my friends experience anything like this, and my mother is slightly worried. Should I see a doctor? I tried heavy pain medication, but it didn't work for me. My mother suggests I go on birth control.