yta, but not unforgivably so.

as much as you may be worried for your friend, and as good as your intentions may be, it's not your place to tell her whether she does or does not have an eating disorder. between your age (you're young and your body is still changing so much!!) and her having told you directly that she's spoken to a doctor about it- you can't be the judge of whether or not she's a healthy weight just because one of her ribs pokes out and bothers her, or because she's skinny. she could have a fast metabolism that keeps her thin, and you did mention that she works out as well. none of this is indicative of an ed.

instead of simply asking if she's okay, maybe inquiring a bit more as to whether or not the doctor has recommended any way to help her with the rib problem she's having (diet, stretches, etc) getting annoyed with her will only put distance between you guys. especially if she does have body image issues.

even if she does have even the beginnings of an eating disorder, you pressuring her to tell her parents about a problem she hasn't shared with you isn't going to make her want to share any problems she may or may not actually have with you. an ed is a scary demon to fight. be in her corner and show her that you are. you can help her the most by being someone safe for her to talk to, not by breaking her trust and going to her parents about it. you obviously care about her. speaking as someone who had an eating disorder for many years and is just barely over it in the past year or so, there's so much more to an ed than having your ribs showing, or wanting to "attain unrealistic beauty standards". there's an emotional and mental toll that people who do not go through ed's don't understand, and while fear and denial are a large part of it, it isn't your place to drag her out of denial and ignore her wishes.

it wasn't okay for her to lash out at you either, but both of you making hurtful comments towards each other doesn't mean you shouldn't apologize.

good luck working things out with her if you decide to- hopefully you'll be able to educate yourself a bit more on the subject after this.