I strugged with this issue (of whether and how to tell) for a while myself, while I was president of my chapter, in fact.
I had told some of the girls that I was closer to about my depression and anorexia throughout the years, but it was definitely something the whole group didn't know about. I was a little bit scared to tell everyone, because while we all got along well, there were some of the girls I wasn't particularly close to (especially the younger ones, who had just recently pledged.) and, like you, I didn't want everyone treating me like I was going to break at any second or worrying about me 24 hours a day.
During my time as president, though, it became clear to me that I was getting much worse, and wasn't going to be able to continue with school. I was going to need to tell my sisters that I was going to resign as president.
The way that worked best for me, was I first brought up the subject in an exec board meeting to not only deal with the logistical aspect of it, but also to kind of test out reactions. They were all very supportive, and it gave me much more confidence to tell the whole group.
So, the following week in our general meeting, I (very tearfully) told everyone what I'd been dealing with and the decision I'd made. Their reaction made so much of a difference in my life, I can't even begin to explain. Everyone was tremendously supportive (I think I got more hugs in that one meeting than in the rest of my life combined). Some of the younger girls (who I wasn't sure how they'd react) were some of the most helpful - I had quite a few of them tell me that they had looked up to me (when I actually thought they didn't like me). I got flowers from the group and a phone call almost every day asking how I was. It was just an outpouring of love and helpfulness like I've never seen before in my life. In my mind, it was the epitome of true sisterhood.
Perhaps even more importantly, and something I was never expecting, was that I had a few girls approach me individually and talk to me about what they were going through and ask me for help. Each one of them said that they'd been having trouble (whether it be with depression, or an eating disorder, or something else) and didn't know where to turn, and when I brought out my problem to the chapter, they realized that they could get help too, and wouldn't be "looked down upon" or anything for it.
So, to make a long story short, don't be afraid to share what you're going through. I think you mentioned that you were a younger member - perhaps you might want to talk to your pledge class and/or big sister first, since they probably know you best - and after talking to them, THEN tell the whole group. I can't tell you how much looking around the room and seeing support in my exec board's eyes helped me get through telling everyone else.
I wish you good luck, and please feel free to PM me if you want help or just to talk!