Any restrictive eating regime can lead to disordered eating in the susceptible. I have a history of teenage AN. That was many decades ago now, but old habits die hard, and it is something I was mindful of when starting to eat low carb. I turned veggie at 13 as well, by the way - it was all part of the same downward-spiral process for me. I'm not saying you'r the same, just that it's a common pattern.
This is what works well for me: eating real, whole foods and lots of them, and highest quality I can afford. Meat, fish, dairy, eggs, vegetables except starchiest ones, olive oil, nuts. This way, I stay a healthy weight and feel strong and my metabolic health is improving. Three good meals a day. BUT, also carrots, parsnips, lentils, berries, yoghurt and whole milk - see next para....
...because here's the thing: in my experience, those of us who are naturally lean absolutely NEED some carbs in order to keep weight on, never mind gain it, as you urgently need to do. You need lots of protein and fat, sure. But if you're like me, you will not be able to keep weight on, let alone gain, if you eat less than 100g of whole food carbs a day.
You are badly underweight, and that is bad for your health now and in the future. And the kind of eating that has got you there needs adjusting, primarily with the goal of getting your BMI to 20 at least, and for that you need to eat a lot more than you're eating now. I think a big part of that will be dealing with a fear of carbs. While your advisors get you up to a healthy weight, they might want you to do more of that than you feel comfortable with. Never mind: getting well is the first priority. Fear of eating is one of the nastiest parts of AN, and eating lots of good food with pleasure and gusto, becoming stronger and healthier in the process is one of the real joys of life. You will recover that joy. But you will need to eat a lot more than you're eating to get there. It will be worth the effort.