As an additional point of clarification in the hope it helps the OP, and based on lack of clarity on this in some of the responses, "NDA" stands for "non-disclosure agreement". A "standard NDA" -- to the extent there are some generally common practices around NDA's -- specifies simply that you are receiving confidential information and that you may not disclose it to other parties.
NDA's generally also specify that you can't use any information disclosed if specified as confidential, and that promise is usually restricted to things you a) didn't already know or develop on your own [and there are various standards as to how much burden of proof there is on this] and b) are not already in the public domain in various ways.
So in a certain way, NDA's can be used to claim ownership over ideas like the one you're working, (e.g. by labelling it as confidential material covered by the NDA and thereby covering "my idea and everything related to it, which I own and you are now agreeing I own").
This would not, however, cover your work, your code, or anything you did without additionally specifying ownership and transfer of rights from you to her in those things.
If the "NDA" specifies that you are an unpaid intern, as yours seems to, this is an employment agreement or work-for-hire contract (to be clear: not a "standard NDA"). If it specifies that you are to turn over code or assign your work, or otherwise tries to retroactively include your work as her confidential material, in exchange for compensation or otherwise, it is an assignment of intellectual property or technology. If it in any way specifies equity or ownership of the company, it's something else altogether.
There are various legal principles and state laws that also could come into play here, depending where you are. (For example, if she's acting as her own lawyer, she might have created a contract that's unenforceable or voidable in various ways.)
It sounds like you're in a strong position and I stand by my earlier answer with respect to how I think you should approach it, but for god's sake don't sign any such thing without having a lawyer take a look, and all of you, please learn what these things are called and what they do.
IANAL, YMMV, etc.