Marion - I have reread your original post, and in it you say that the song you have written is from the point of view of the mother singing to the baby. It seems to me that you are writing the song in the abstract then, rather than specifically about the lady whose experience sparked off the inspiration. You aren't seeking to reproduce exactly what she, personally, was thinking & what she, personally, would express to her child. So I think you are in no way exploitative. You heard her story, and it inspired you to explore that situation emotionally and to build a song - but that song comes from your emotional response to the concept, not hers.

I don't think you should tell her that you have written this song about her - I think you should tell her that hearing about her tragedy made you think deeply about the loss of a stillborn child, and that those thoughts inspired you to write a song. You could ask her whether she thinks the song is appropriate - but then maybe she might not like being put on the spot like that.

In any case you are likely to tug at some very strong emotions with this song - so you need to be aware of that when you sing it to people. For some it might be very painful, and of course there's always the possibility that some audiences will be put off by such strong emotion & will just switch off - so you might have quite a polarised audience!

Best of luck with whatever you decide to do with the song