I believe it would fall under EDNOS (Eating Disorder not otherwise specified), you would need to talk with a specialist to know for sure, what you described sounds sorta like anorexia binge/purge subtype, but again, you would have to talk to your medical team and show them your diet and whatnot for them to make a diagnosis. There are several different types of eating disorders in addition to the most "common" ones (Anorexia, Bulimia, and Binge) which is why they cam up with EDNOS as an umbrella term so more people could get help. If your eating patterns are a true eating disorder (and sounds like it is since you have a history of other addictive behaviors) then I don't believe any hormone changes will make much of a difference. My ED team has repeatedly told me it's not actually about your weight/size/appearance, that is usually just what the ED tells you to distract from the real problem. The brain of a person with an ED is wired differently than the "normal" brain, so it has to be retrained to think differently. No matter what your body looks like until the brain is retrained, you will never be satisfied with how you look. I do think you are making a huge step by acknowledging that you have a problem and are making an effort to do better, but I would strongly encourage you to try and talk to your doctor again, if he/she still doesn't understand, tell them you want a referral to a specialist. It's VERY hard to do this on your own.
I have anorexia binge/purge subtype and my "binges" do not fit what most people consider a binge either, but it IS a binge for me AND I don't tolerate gluten well, but when I'm binging I tend to eat lots of gluten which makes me very sick. And every time I say "I am NEVER eating gluten again!" very next binge I'm looking for gluten. So you aren't the only one eating stuff that makes you sick, I'm sure there are lots more out there that do it, too... doesn't mean it's healthy, but it helps to know you aren't the only one with a problem.
I'm going to quote my doctor "A lot of times with eating disorders, you're fine, and then one day you're not anymore because your body is worn out, once the warning signs start, it's a major issue and things go downhill very quickly". Please don't put it off, it's not worth the risk.....