Eating issues with 13 year old

My daughter is 13. When she was younger she carried a fair bit of baby fat, and had a few kids tell her she was fat, but in the last couple of years has lost all that and has started exercising and rowing. However, she is taking things too far.. she barely eats for fear of putting the weight back on and over exercises to the point where she exhausts herself.
We have talked to her about her thinking and how to manage these thoughts, where they have started from and how to just let them be and carry on with her day, but I see her eating and struggling with her head and what it’s telling her about what she’s putting into her body and it terrifies me. I genuinely fear she will develop a full blown eating disorder from this, although I don’t believe she will go down the bulimia road as she hates throwing up. I prepare her lunches and tell her she must eat it (all low fat and healthy options) and let us know what she ate that day, I sit with her at breakfast and we eat together just so I can make sure she eats enough, without making a big deal out of it as I know that will push her away. Same with dinner times.
I don’t know what else to do, we have a doctors appointment tomorrow and I’m hoping she’ll open up, if not I will. I just want her to be ok, and that happy bright kid she can sometimes be when she let’s go of this fear even just for a while. In the meantime I’ll be there for her, every day, every step of the way but man this is so stressful and hard to watch 😢 Anyway thanks for the vent, any positive advice would be great. I don’t need the horror stories thanks, I am aware how far this can go without intervention.