Am I already healthy?

I'm a girl in her late teens, slightly less than 5 feet tall, and slightly less than 90 lbs. I missed my last period and my hair has been falling out. I did have a little bit of brown for one day this past month, but no actual blood. My parents believe I'm underweight and want me to gain weight. I know that when I was about 13 or 14, I weighed around 97-98 pounds...then I had an almost eating-disorder for a few years and went down to 80 lbs. I weighed around 96 lbs before this summer, because my parents made me eat more to regain weight. I like the way I look, though...my face doesn't have as much baby fat as it used to, for example, and so I don't want to gain weight. I just don't know if I'm supposed to. My dad's in the medical field, but he's not a nutritionist, and he refuses to take me to one because he feels very strongly that I must gain weight. I sometimes wonder if I stunted my growth with that eating disorder--I'm also quite flat-chested, but so is my mother. That could just be genes. Medical advice?