This is definitely disordered, and talking to a professional might be helpful. Look, EDs aren't all about food - food is just the outlet used. There's always something else going on, and ignoring whatever it is that's going on, for the sake of not having to gain weight is going to make your life so much harder in the long term.
What's likely to happen here is that you might start seeing a school counsellor, or go on the waiting list for CAMHS, and you'll need to eat enough to maintain your weight. If your doctor encourages you to gain weight, you're looking at about 5lbs, maybe a bit more - which honestly? No one will notice, likely you won't even notice once you've gained it.
Also, fainting so frequently in one week is definitely worrying - I know multiple people with restrictive EDs, and fainting has still been pretty rare for them. Are you sure you're properly hydrated? Especially when you're not eating enough, staying hydrated is really important, so I'd consider trying to drink more throughout the day.
Hopefully this helps, and I hope you find someone to talk to!