Hi Jasumi,
in most of my dreams I meet old friends, and/or there are components which I currently deal with in physical life, and then there are dreams of a different kind.

Yours seem to be not drawn from your present life- I think it would be not likely for a girl not older than 8 years to have this dream several times, only because of hearsay or media reports of  the giving birth process.
So, maybe it was a piece from a past life. When I read about (what they think is) past-life memories, dying while giving birth came across more than one time. I think it is not just coincidental; it could leave a very strong emotional impact and attachment, as especially this way to die is connected to "Not now! I can't leave my child alone!", so it may be such strong, traumatic, that it passed the veil of forgetting.

The anchor points of unreveiling some of my own (seems-so) past lifes have been always traumatic, or at least emotionally charged and/or problematic moments.

Spooky