Could these be signs of an eating disorder?

I have noticed a lot of these signs in my sister:
-she says she feels guilty when she eats
-she "punishes" herself when she eats too much
-she looks at every single calorie she eats and counts them
-she says that she is fat even though she isn't (she's about 5'10 and weighs 127-129 lbs)
-she has accounts on almost every single dieting site.

what should I do? how can I help her? if i tell her to go see a doctor she will think that I'm jealous! Please help me!

Sounds like she's at risk for oneWell, don't just tell her she should go to the doctor. Talk to your parents or school nurse.
most definately sounds like an eating disorder...i dont think theres anything other ppl can say to make it better but encourage her to get help
omg that is a big sign.. try to encourage her to eat and if that doesnt work get ur parents to help they always know what to do.. it could also be medical so try seeking a doctor!
she definatly has an eating disorder, she needs help. soon.
the punishing part is pretty weird. also, if shes serious about calling herself fat, then thats not good either. everything else is pretty normal. try approaching her casually.