All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
It is permissible to recite whatever you have memorized of the Quran after giving birth to your child according to the scholarly view adopted in Islamweb. You should know that scholars held different opinions in this regard. The Kuwaiti Encyclopedia of Fiqh reads, “The Hanafis, Shaafiʻis, and Hanbalis maintained that it is prohibited for a woman to recite the Quran during menstruation or post-partum bleeding, as evidenced by the hadeeth that reads: 'No one who is in a state of janaabah (impurity after sexual activity) nor a woman who is menstruating should recite anything of the Quran.' The Maalikis, on the other hand, held that it is permissible for a woman to recite the Quran during menstruation or post-partum bleeding.” For more benefit, please refer to fataawa 181903 and 83772.
There is no problem with listening to the Quran or reciting or listening to religious poems; none of these acts require a state of ritual purity to begin with. It is also allowable for your husband to recite the Quran over you at any time, whether during menstruation, post-partum bleeding, or any given state of impurity; you experiencing the post-partum bleeding or not has nothing to do with the permissibility of reciting the Quran over you.
As for your question regarding the specific thikr (remembrance), supplications, or chapters of the Quran to be recited to ease the woman’s labor pains, there are some reported ruqyah (healing through Quran and supplications) that may help ease child delivery that were cited by Ibn Al-Qayyim :
“Easing the pains of labor: Al-Khallaal narrated on the authority of ʻAbdullaah ibn Ahmad that he said, 'I once saw my father (Imaam Ahmad) writing the hadeeth reported by Ibn ʻAbbaas on a white drinking cup or a clean bowl, for the pregnant woman when the pains of labor worsen. The hadeeth reads, 'La ilaha illa Allaah Al-Haleem Al-Kareem, Subhaan Allaahi Rabbi Al-ʻArshi Al-ʻAtheem.' (None has the right to be worshipped but Allaah, the Forbearing, the Most Generous; glory is to Allaah, the Lord of the Mighty Throne.) Then, he would write, 'Alhamdulillaahi Rabbi Al-'Aalameen,' (All praise be to Allaah) and then the following verses of the Quran:
- {It will be - on the Day they see that which they are promised - as though they had not remained (in the world) except an hour of a day. (This is) notification.} [Quran 64:35]
- {It will be, on the Day they see it, as though they had not remained (in the world) except for an afternoon or a morning thereof.} [Quran 79:46]'
Another ruqyah is to write the following verses in a clean bowl for the pregnant woman to drink from the water therein and have some of it sprinkled over her belly: {When the sky has split (open), and has responded to its Lord and was obligated (to do so), and when the earth has been extended, and has cast out that within it and relinquished (it)...} [Quran 84:1-4]'” [At-Tibb An-Nabawi (Prophetic Medicine)]
As for supplication in general, it is prescribed for the Muslim to implore Allaah at any given time or state, especially when calamity befalls. Allaah, The Exalted, says (what means):
- {Is He (not best) Who responds to the desperate one when he calls upon Him and removes evil and makes you inheritors of the earth?} [Quran 27:62]
- {And your Lord says, "Call upon Me; I will respond to you." Indeed, those who disdain My worship will enter Hell (rendered) contemptible.} [Quran 40:60]
Allaah knows best.