(((((((((((TPND))))))))))))))
I'm worried about you dear. Not to make you feel guilty, but you really need to tell your GP the truth about what's happening with you. Get inpatient treatment if need be, talk to a counsellor, get on antidepressants, get to a selfhelp group - whatever it takes to take care of YOU.
Throw away the magazines. Tear them into little tiny pieces (good form of "release" that's healthy) and throw them away. You don't need to listen to that voice - I know it's tempting because it "understands" you... but please, hold on and listen to someone else -
"I am okay the way I am"
"I don't need to lose weight."
"I am healthy right now, and I don't want that to change".
"I am worth seeking help for".
"I'm a good person and worthy of love and respect"
(and whatever else you can think up.)
Write all of those down. Make a new and better poster - write down positive affirmations to yourself. Positive meaning HEALTHY and GOOD, not anything else.
If someone else was in your exact same position, you'd try to help them control their behaviours, right? Try to do the same for yourself. You're not unworthy, you are not sub-human and you ARE ultimately a good person.
I know our behaviours hurt others. Sometimes that's good motivation to stop our negative behaviours. Sometimes, but not always. How about writing down how you're hurting others, but also make a list of how you're hurting YOURSELF by continuing this pattern of behaviour?
Eczema isn't very cool... unfortunately it's likely to come back randomly, especially if your immune system is compromised. It's like having a coldsore on your lips - when you're stressed and not eating/sleeping properly, it's more likely to wreak havoc on your system.
You DO have some control. You can say: "I've had enough" and "I want to quit doing this". Anything after that means that yes, you're going to be having a control competition with your eating disorder and all that - but you can still win over it. It just takes a LOT of work.

You're trying. That's a good first step. You realized you don't have as much control as you'd like in this situation, that's also a good step. You're reaching out for help, that's another good step. One step at a time, and yes sometimes you will backslide a bit - but you're much more prepared for any setbacks in the future that way if you know what to expect.
I'm sorry that Connor is struggling so much in trying to help you. He sounds like a very nice man... but he's responsible for trying to help himself. YOU need to work on helping yourself first. We can't help others unless we help ourselves, really.
I think you should go to your local hospital and ask for some treatment and support right now, ok? You sound like you're needing help, and that's NOT a bad thing - but unfortunately I can only say/do so much.

please take care of yourself. you are important and cared about here.