Well, if you go strictly by numbers, to meet diagnostic criteria for anorexia you have to be at least 15% below your ideal body weight.
At 5'2, your ideal/healthy body weight is approximately 110 pounds.
15% below that is approx 93 pounds - that is anorexic for your height.

Your current weight being 82 - means you are 25% below your healthy body weight.

So yes, I would say you are anorexic.

Numbers aside, it sounds like you have a distorted body image and a fear of being fat. Even though you are still eating some, you are not eating enough to maintain a healthy weight. Most women burn at least 1200 cal a day just for the bodies to function, and then if you add in exercise you are burning a lot more.

Have you talked to anyone about this? It would probably be wise to talk to someone supportive in your family, your doctor, or a counseler. I've heard that the longer you struggle with this, the hard it is to recover because the behaviors become so ingrained and addictive. It is best to get help early.
Good luck to you, and take care, Girlish.