Do I have a problem and should I see a doctor?

I just need some impartial opinions here. Recently a lot of my friends have been commenting on my weight and eating habits. I said this to my mum and she said she thought I should eat more, but she doesn't seem to understand it's not that easy as food makes me feel anxious. I feel like I'm two different people: one who is very focused on restricting food intake and one who is aware that my eating habits are a bit odd. In the past 8 months or so my weight has dropped from 138lbs to around 106lbs, and I'm 5"2, so I'm not underweight. I have been eating progressively fewer calories during this time, now rarely eating more than 500 and often eating under 300. If I do eat too much I use exercise and laxatives to avoid weight gain. I weigh myself twice a day otherwise I get anxious. I tried to tell my mum that there is a bit of me that's concerned about my health - I am constantly cold, often dizzy and my periods have stopped - but I found it hard to be straight with her and I'm not sure she really understood what I was getting at. I don't know if my behaviour is normal to others or not, as it is just how I live now so obviously it's normal to me. The side of me that's worried would like to seek help because I'm worried that my period's stopped but I'd be embarrassed if I didn't really have a problem and I'd wasted the doctor's time. I am a 15 year old girl.