Percy I'm too lazy to explain all of this and will just assume that your knowledge of objectivism and the key players is pretty good.
The crux of the question is "do I have a moral obligation at all to avoid running this little girl?".
Because I am dead set on suicide and wish to get it over and down with, then in this siutation I am confronted with a source of obligation besides my own choice (axiomatic or otherwise) to live one, indeed, it is one that is altogether independent of my choice, and one that sets limits within which my suicide can be carried out.
Since Rand denies that I have any such obligation, she must also deny that the well-being of persons other than myself directly imposes any sort of moral constraint on my behavior.
Quoting Scot Ryan's book on the subject -
David Kelley has noticed the difficulty here. As regards rights, he acknowledges that even if I understand that your freedom is good for you in exactly the same way that my freedom is good for me, I don’t yet have a reason for regarding your freedom as good for me. But this is precisely the point that must be established if we are going to validate rights on the basis of ethical egoism [How Principles Work, in Liberty, November 1992, pp. 63-76; quoted in Jeff Walker, The Ayn Rand Cult, pp, 235-236]