Serious question- is 5'5" and 107 lb fat? or chubby?

I always thought I was thin, possibly too thin, but a ton of stuff came up on an anonymous message board about how fat I am and how I should diet. I'm pretty dubious about this being true, since according to BMI I'm underweight, but the model from Ralph Lauren who was fired for being too fat was 5'10" and 120 lb--thinner than me by BMI! So I really don't know what to do. And no, I do not want to be "average" , I want to be thin. And if this isn't thin, I will lose weight. But of course, I wouldn't want to be dangerously thin, to the point of losing my hair or any curves.