Can you have sex when you have your period? If so, how?

Since becoming sexually active, I feel like my menstrual flow has changed and that my cramps have been worse. Before, I hardly had any cramps but now I really feel pain during the first day of my period.

Is there anything other than birth control that will help lighten my period and relieve cramps?

I have horrible menstruation. Horrible. The cramps make me cry and be nauseous (I've had to stay at home on more than one occassion for them and I NEVER miss school), the blood flow is relentless (7 days usually), and I get a severe headache and mild fever. I have a suspicion that it's genetic, considering how my mother once bled for 12 days. Exercise seems to help, but I was wondering what else I can do? I'm sick of feeling like this a week every month. I'm at the end of my rope!