I am having severe pain on my left side, right over my ovary. I have also had nausea along with headaches. I have thrown up 3 times in the past day and have been having hot flashes. Sometimes the pain gets so bad I have a hard time walking. Pain medicine does NOT work at all. Have any idea what it is or what I should do? I am 16 years old and female.

If I were you with those kinds of (very serious!) complaints, I'd tell a parent and make a doctor appointment for, like, yesterday or go to the ER. No one here can diagnose you. You've got to be checked out by a real-life doctor -- and be sure to tell him/her ALL of what you have been going through.

You are a minor child, under 18, so you tell a parent or guardian.
The abdomen (female especially) has far too many organs and conditions to sort any of it out online. It's hard enough in a doctor's office. And pain can refer from one spot to another.
So why are you asking us instead of telling a parent? If he or she or both are at work, call one of them and ask them about either calling your family doctor or meeting you at an ER, or both. You are old enough to call the family doctor, but call a parent first.

I have gone to the ER and they haven't found anything.. they send me home with pain medication and say they have no idea why I am having pain.

That's the ER... not your regular doctor or a substitute for them... they are there to treat emergencies... your doctor (primary care physician) will know your medical history and be able to spend more time with you.