What is the ruling on a vow made with the intention or an inaudible utterance during a difficult childbirth, knowing that the vower is currently unable to fast due to breastfeeding and illness?

As long as you did not utter the vow with your tongue, your vow is not binding, because a vow is not binding merely by intention; rather, it requires utterance with the tongue.

Similarly, if you are unsure whether you uttered the vow or not, then nothing is required of you, because the default is that the vow is not binding.

Therefore, you are not obligated to fast the aforementioned days because your vow is not binding.