My friends think I'm anorexic...?

I'm 16 years old, 5 foot 5 and 103 lbs. I can't stand the feeling of food being in my stomach, and when I do eat something, no matte how small it is, I feel insanely guilty and I have to workout right after or I freak out. I exercise for an hour everyday and eat very little, if at all. I skip multiple meals and avoid hanging out with my friends if it involves food. Also my boyfriend is always telling me how gorgeous I am, but I don't believe him. Am I anorexic? My friends seem to think I am, but I'm not totally sure.