It looks to me like both you and your girlfriend need to seek medical attention; you for your memory and her for her eating disorder. As for the situation with your girlfriend goes, don't listen to any of her threats. She has a serious problem, and coming from experience, I'd advise you to get her help as soon as possible. When I had a friend with an eating disorder, she blackmailed me and threatened to end our friendship. She didn't mean it, she just felt as if she had no other option. It looks to be the same situation with your girlfriend. You said you two are close, so you're probably familiar with her family. Try talking to her parents one day alone and tell them about her eating habits and how worried you are. Chances are, she'll get the help she needs and she'll thank you in the end. If not, like you said, you put yourself out there and tried your best.
Your short term memory loss seems to be a huge problem between you and your girlfriend. Although you shouldn't have to remember her eating habits. You're not her keeper, and although you want to help her, she needs professional help too. Maybe you can work with her through her recovery, but you also need to take your health into consideration. You sound pretty young, and sometimes, us teens don't have the best memory. It could be something far more serious, though. I'd definitely go get it checked out. I'm not a doctor, so I have no clue what this could be a symptom of. I don't want to worry you, but since your lack of memory is really stressing you out, I'd go to a doctor as soon as possible.
Your girlfriend has a serious problem, and as much as you love her, you shouldn't feel guilty for it. You're trying to help her the best way you know how-by supporting her. Instead of allowing her to blackmail you, do the same to her if she refuses help. If she doesn't get the help she needs, tell her you won't be able to see her anymore. It's a tough thing for any girl, or guy for that matter, to go through, but eating disorders can be worked through.
I wish the best for you and your girlfriend. If you need anything, feel free to PM me.