Requested no pitocin (oxytocin) be used during labor. Rn says they'd give it after birth. Is it common to be given pitocin (oxytocin) after delivery? Why is this necessary?

Yes, it is. Standard, the most common source of bleeding after delivery occurs when your uterus does not contact and you bleed heavily where the placenta was implanted. The goal is to prevent hemorrhage, it is safe and commonly used. Good luck.
Prevents death . Bleeding after delivery (post partum hemorrhage) throughout human history is one if the leading causes of death in women. Fortunately in first world countries this has been greatly reduced by giving Pitocin (oxytocin) after delivery of the placenta. This is a well proven intervention that saves lives. Be careful deciding to deviate from the standard of care based on myths you may have read on the internet.