Please someone help- do I have an eating disorder?

This past year I've gotten thinner because I stopped being sedentary and started eating better. So it started off just being healthy weight loss. After losing 20 pounds, I was really thin but not happy because I had a desire to be underweight for some reason. I do eat...I don't starve myself (i.e eating below 1200 cal) but I eat a significant amount less than what is recommended for my age, activity level, and height because I'm absolutely terrified of gaining weight. I count every calorie that goes into my mouth even if it's just gum or tea. I find myself always recounting my days worth of calories to make 100% sure I didn't go over the limit I set myself. I exercise solely for the purpose of burning calories...I don't actually enjoy it. I once tried to make myself throw up after eating too much last year and haven't had trouble with that since until yesterday. I ate over my calorie limit and I had really strong urges to make myself puke. I kind of think I have issues but I don't know I'd get help since my BMI is 18.6 so it's not low enough to be considered for therapy or anything and maybe this is all normal? I don't know, is it? Do I have something wrong with me?