I think there are separate issues here.
I think it might be wise to schedule a double appointment with your GP, if they allow that, to be able to chat things through.
I think, especially with your anxiety and being so slim, they may see a link with food. I had a GP tell me I had an eating disorder and tried to refer me to a specialist a long time before I realised it.
Try not to stereotype, it's what it says, a problem relation to food and not necessarity the sterotypical versions think of like anorexia and bulimia.
It may be your anxiety is interfering with your relationship with food, often feelings can manifest in strange ways where you might not even see a link and if your system is stressed from anxiety it may not be functioning at it's best when it comes to eating and digesting.
I think your anxiety needs addressing which is one issue you can raise with your GP. They can help with medical support if needed - don't be scared of medication - think of it like a drug to treat a chemical imbalance, it's science, like you'd take a paracetamol for a headache.
Waiting lists can be long on the NHS and, as it sounds like you have really supportive parents, would they consider paying for you to see someone privately? GP's often know of people who are really good.
My GP suggested a private cognitive therapist to me and, although dubious about it in general and the cost, she is absolutely fantastic and has made a huge difference to me.
It's not scary, just gives you a chance to talk and it's really all about you and finding balance and coping strategies and such.