Hi binth I am sorry to hear about your daughter. It really does sounds like she has an eating disorder, I hope you can go to the GP soon and 'get her in the system' for dealing with it.
That your daughter says she wants to eat and is sick of not eating properly is only indication that she is saying things to placate you. Eating disordered people are very sneaky and will do anything to keep their illness. the control they have over not eating makes them feel safe, even powerful, it is their naughty secret and makes them 'happy'. it is like an evil twin that they love and loathe in equal measure. It is all about sadness and anxiety, essentially as other posters have said; the illness tells them that they will be a better, kinder, happier, more popular, loveable person if they are thin, thin, thin. However, the sadness can also be hidden behind a smiley personality! It is so tricky, I feel for you OP. They will 'lapse' from the control and, like any normal human, give in to temptation and eat and eat and eat, especially treat foods. This is quite normal.
Some signs of serious anorexia can be seen in depression (if she is not hiding it), is she a high achiever with perfectionist tendencies, does she take food and hide it (they can hide things to test their resistance and, of course, look like they ate to others), does she have a weight diary, does she go on anorexia websites?
Whatever is going on your daughter sounds poorly, either physically or emotionally, and needs some help from you. Good luck OP, I really hope you find the above all have absolutely nothing to do with your daughter.