Do I have an eating disorder? If so, what is it?

I am at a normal weight for my age & BMI and body fat percentage, but I still feel fat. I count calories and starve myself sometimes. After or when I eat something with a lot of calories or an amount I consider a lot of food, I feel guilty but I don't stop myself from eating it. I exercise excessively rarely but I am proud when I do. Some people tell me I'm perfect, thin, or too thin. I don't tell them that I think I'm fat. Nobody knows that, I feel highly embarrassed to tell anyone. I have wanted to be underweight. When I was younger I was underweight but then in 3rd grade I was at a healthy weight.
I used to not even think about fat or anything but now I think about it all the time. When I see people that are overweight I think fat. I measure myself (waist, hips,ect) when I worry I've gained weight. I can't stand wearing baggy clothes that make you look bigger. I always read the calorie content, fat gram, sodium ect. on any food I'm eating. When I'm in public, and I'm hungry like after a while but we are like in a store or car, I will not eat if people or looking/if the window is rolled down. Rarely I hide food & eat it really rarely. Rarely, I spit food out into my napkin & act like it was too hard to chew or I go to the restroom and get rid of it. I lie about how much I ate sometimes. I have really low self esteem/ body image is horrible. I compare myself to this girl, who is really pretty. My friend calls her fat because she considers herself (my friend) fat & she is a little large and she has called me fat but shes joking. I don't take it seriously. Once I was walking with my "friend" and some girl I didn't even know said I was fat (I think she said that, but I just acted like she didn't say it to me/ I didn't hear.) Also that day I had some guy I didn't know whistle at me. When I felt really bad I didn't eat a lot. Also I have a friend who starves herself, who I consider thinner than me. She calls me thin but her fat. Most of the days, except which I have school on, I skip lunch.