Hi Penelope,
Thank you for your post. I'm sorry to hear about your struggles.
Firstly, it is okay to not feel okay. Many people suffer with frustrations about their body, or are unsatisfied with certain body parts, so it is important to realise that this is common place. That said, there is having issues with your body and having a disordered view of your body, which an eating disorder can force. I know it is hard, but while you are poorly, body checking can hinder things significantly.
I wanted to address you concern around fluctuation. You have described a fluctuation of 5 pounds (less than 3kg). Fluctuation happens all the time. Your weight never stays stable, because you can eat, drink and do exactly the same thing day in day out, but due to air, heat etc you will still experience a different number, one day to the next. Where you don't do everything identical, you will experience even more of a fluctuation (e.g. drinking more tea one day, and less the next) and furthermore on your time of the month. Here it is important to recognise that these are all natural processes, they are not weight gain, but merely a change in water shifting around your body.
One of the things that can affect weight change is restricting followed by bingeing. What restriction does it puts your body into safe mode. It realises it is under pressure / unsafe so everything slows down. It means that anything you eat, it is more likely to store - this is a basic means to survivial. Your metabolism slows down, and so your weight loss plateaus. This has happened to me numerous times, recently I was eating far too little due to difficult events, and my weight went up. My dietitian enforced a higher calorie rule, and guess what...it went down. (This isn't good, because I need to be gaining, but it is reassuring to know that my metabolism speeds up as I eat more of a normal amount of food).
One of the main reasons for bingeing will be your restriction. So in a nutshell, to stop it you need to stop restricting. If you hold your breath for a while, when you start breathing your breath becomes short in order to catch up. The same is when you deprive yourself of carbohydrates. We need both oxygen and carbs for respiration, so if your body is missing carbs it will try and find it in its most dense form (like the short breaths), thus leading to bingeing. Again this is natural process and very difficult to avoid. To solve, you do need to eat regularly with carbs. It has taken me years to get to this point, but I don't binge now. It is worth looking at the Minnesota study which explains the effects of restriction.
Finally, it is clear that you feel that health professionals, your family and friends are against you. This is very normal and it is evidence that your eating disorder is stronger than you right now. Your eating disorder is telling you that everyone around you is jeopardising your plans, and beating you up mentally when you don't do what it wants you to do. You are feeling pleased because of your weight loss, but its a catch 22 situation because once you lose weight, your eating disorder isn't satisfied. I know you don't want to hear this, but you are not in control, your eating disorder is. My eating disorder has had enormous impact on my life, to the extent that I nearly took my life. If you carry on this way, you won't make it to university, or if you do you will probably end up coming home because you are too ill, and hating all the while you are there. I'm glad to hear your parents are concerned, because it means they are on your side. It is a great idea to use theirs and the health professionals support.
Looking at your measurements you are actually underweight, and you should be looking to increase to a BMI of between 20 and 25. The 18.5-20 bit was added on to cater for some of the Asian population who have a lower bone density. Your eating disorder is telling you you are fat, when science is saying otherwise.
In conclusion, my advice would be to start thinking about everything you will lose out on. What are the pros and cons of staying with your eating disorder and recovering from it. After this it might be helpful to see a therapist so you can understand why. Eating disorders aren't diets, but coping mechanisms (bad ones...) for difficult experiences.
Good luck.