I think Keith has the right of it, in that she isn't really ready for a poly relationship. The whole "you can only have sex with me" rings of insecurity and is often used as a method of controlling a partner.
That said, there are folks who have that sort of arrangement. The difference between what you've described and what those folks have lies in the realm of maturity. They know themselves well enough to negotiate the terms of their relationships with solid understanding of what's involved. As you've described it, your girlfriend doesn't know herself well enough to engage in that sort of negotiation.
It sounds to me like she's OK with you having other close female companions and just scared that you'll leave her if you have sex with one of them. Or she's bought into the childish notion that if you really love her you wouldn't want to have sex with somebody else.
I'll suggest that you simply take enough time for both of you to get to know yourselves and deal with your own baggage--insecurities and such--before worrying about adding anybody else to the equation.