You aren't a shit friend if you tell her you can't do it any more. Current ED suffered with a very long history starting in earlier adolescence, with various ups and downs here.
First thing to note is that the only thing an A&E visit will yield is a chat with a psychiatrist to check she doesn't need to be sectioned, and if she's dehydrated or in electrolyte imbalance they will put her on a drip to fix that. They won't get her to eat if she doesn't want to. Saying she will be sectioned if she is at a BMI of 13 is inaccurate - the bar for sectioning is so incredibly high now. She'd have to be at such a parlous physical state that going any longer without hospital treatment would kill her, and there is quite a lot of case law affirming the autonomy of very sick sufferers even when their eating disorders threaten their lives as well. If she's relatively new to this and has suffered significant health problems, a short admission to rehydrate her might shake her up a little bit. Unfortunately, don't expect health professionals to step in urging help and providing plentiful support. Even if she willingly goes to her appointment and appears quite sick, she'll also have to demonstrate a lot of willingness to change to access and keep accessing treatment.
EDs are also highly egosyntotic and everyone believes it won't happen to them - whether "it" is sudden cardiac death, oesophageal rupture, hair falling out, symptoms such as bingeing and/or purging, and so on. In my case it was osteoporosis - I knew it was happening logically but didn't realise what the impact of that would be. Broken toes were acceptable and so were broken ribs - until my punctured lung collapsed. Losing feeling in my feet was scary but OK until I connected it with a severe spinal fracture. My dominant arm shattering like chalk after an insignificant tumble off a pushbike was... well, totally physically disabling, still painful and stole my life for six months. My nose also broke and I was lucky it wasn't my skull.
Two other points I want to make: there are commonalities between ED sufferers, but many more differences. When you know or have been one person with an ED, you know one person with an ED. None of us know your friend like you do and like her family members do, so I'd go with her instinct, coupled with clues others are giving you, instead of relying on blanket statements. There's also a twofold effect in responding with things like "you look gaunt" or "I'm worried". On the one hand, particularly with new sufferers, younger people and particular personalities, they do "get a kick" out of it and it will worsen things because they will feel like they want to keep getting this, in their mind, positive feedback. On the other hand, not reacting at all can make you feel like you're "not good enough". I've never been someone who loses weight for aesthetic reasons, so the compliments I received around a BMI of 14.5 were more worrying and perplexing than anything. However, people ignoring my weight - I always hid restricting and purging behaviours - led me to believe that I wasn't being good enough or punishing myself enough for my eating disorder. If nobody says anything (and your boyfriend at the time is sleeping with you even though you look like a starved dog) and then someone says offhand that you're too thin, it's much harder to accept it. I would advise maybe don't say anything unless it's called for by the conversation, and if you're responding to any fishing by her, say something factual and fairly neutral.
If you want to keep in communication with her, or even if you don't, this may be controversial but think about having, again, a very neutral and factual talk about how this is affecting you. Say you know she's fishing for validation, acknowledge what she's going through and then tell her what a huge emotional toll it's taking on her. Not emotional blackmail, or telling her off, but try to combine acknowledging her physical state and her own suffering while making her aware that as someone who cares about her, it's making things incredibly difficult for you. Whatever you decide, at the very least, you should have boundaries in place. I don't want to say EDs make you selfish in the true sense, but they result in you becoming incredibly self-involved and doing things that hurt people even if you don't mean to. Don't accuse her of doing it TO hurt you or not caring about you, that's likely to backfire and in some cases making people feel guilty makes them want to starve and punish themselves more. It depends on what sort of person she is. But you need your own oxygen mask on first and sometimes people genuinely don't know they are causing others worry (some know very well and don't care, or want to "win" at weight loss, and I don't really know what to say in that case).
You don't have any obligation towards her. She might want and need support, but you can only do as much as you can do, if that makes sense. I personally don't believe tough love works for the sufferer, but self-protection for people who know and love them is absolutely essential. Many people have had to distance themselves from me over the years - not just over the ED - and rationally I completely understand that and don't resent them at all, I just miss them. Of those who have stayed around, the most helpful are the ones with strong boundaries.
I went through years with my sister when she saw I had dropped a lot of weight after my first term at uni and decided then and there to diet, plastered her wall with pictures of supermodels, got on pro-anorexia websites and promptly ended up with anorexia. I could see the signs from day one and literally went mad trying to alert my parents and family members, being gaslighted, manipulated and bullied in return, and my sister blames me entirely for developing the illness in the first place because I lost weight (I was five years into severe bulimia at that point). I would not wish that on anyone. It's pure emotional torture. However, the people who can and should do the most for your friend are her family, biological and by marriage. I'd make your feelings known at least to her OH and any other family members you're close enough to. Normally I would frown on talking about her behind her back, but if you have mutual friends you could share your feelings and concerns with them.
Unfortunately she's an adult. You can't make her do anything. I'm sorry this was so long - you don't have any responsibility to her, except that in the end you do have to put yourself first. Best wishes to you, and take care.