I think that many serious distance runners can identify with your struggle. You haven't told us a lot about yourself, but any astute observer who has worked extensively with young, driven, female distance runners probably has a pretty good idea of what you are going through right now.
I think it's important for you to understand that the physiology of fast running -- and, more importantly, the physiology of good health -- involves a lot more than manipulating the levels of muscle and fat in your body. Over the long term, to progress as a runner, you need to be a healthy animal. My guess is that, right now, you are not a healthy animal. I suspect that your bones are porous and fragile. I suspect that you are seriously depressed. I suspect that every breeze on an autumn afternoon causes you to shiver. I suspect that you go through each day feeling light-headed and weak. These are not the ideal conditions for developing as a runner and, more importantly, as a young woman.
In the short term, I don't know whether gaining weight will speed you up or slow you down. Nor do I know how much of the additional weight will be in the form of muscle, or fat, or bone, or blood, or an increase in the size of various internal organs (such as your heart). But I'm fairly confident that, over the long term, staying at on below your current weight will hurt your running. It could even kill you. I'm pretty sure that your doctor and others have already told you that.
In my opinion, what you are struggling with is very complicated, both physically and psychologically. I will simply suggest to you that your goal right now should be to get healthy, physically and mentally. Faster running will come later, but only after you get well.
By the way, I was going to suggest that you might want to talk to other young women who have been in similar circumstances. I thought that something like fast-women.com might be a good place to find others. I then came upon this thread:
http://web1.nyrrc.org/ubb/Forum2/HTML/000693.html
Is that you?
P.S. I hope that you will keep us informed of your progress. I, for one, am rooting for you.