Your description sounds like your uterus didn't begin contractions to stem the (normal) bleeding associated with delivery of the baby/placenta. When your body begins to contract the uterus after the baby/placenta are gone, it begins to stop the bleeding. It's the beginning of the post-partum recovery. Think about it... you will bleed for some time after the baby is born.. sometimes the entire 6 week post-partum period. For some people it's longer than that, for others it is more like 3 or 4 weeks. During this time is when your uterus is returning to its original/normal size. That's what the doctors are checking for (mostly) when you go back for the post partum checkup. I suspect your failure to "contract" after meant that you had a lot of bleeding (hence passing out ?). Most deliveries end with the mom being given pitocin (even in a normal natural labor) to speed the mother's uterus contractions to stem the blood flow. Being given iron was probably b/c the excessive bleeding (from your uterus not contracting quickly or strongly enough) caused you to be anemic.
I didn't have a c-section, mine were born naturally, and the nurses were very hesitant to let me stand up right after (without help) b/c they were afraid I would pass out (common issue they watch for, due to blood loss during delivery). I'm sure that with a C section, you also had medications that may have contributed to a drowsy feel, even without blood loss, but couple the two....
Next time you are at the doctor's office, talk to him about what happened and the odds of a recurrence. I don't know that it is hereditary... just something that happens sometimes. But talk to your doctor if you are concerned about the risks of another pregnancy.