Will my pain medication after birth affect my babies feeding?

Depends. Most prescribed or recommended by an experienced OB will have little effect on baby. Even those with some hydrocodone will not pass into the milk in enough quantity to bother baby if used cautiously.Some sedation would be expected if you use the maximum amount prescribed. I've seen one baby admitted for low body temperature and weakness when hydrocodone containing med was taken every 4 hr.
Check. Check on the medication you are being prescribed. Let your doctor know you are breast feeding and ask for pain medication that will not affect your baby. All the best.
Depends on the drug. Acetaminophen and ibuprofen for example are safe with breastfeeding, unless you're not allowed , ask your obstetrician, enjoy the new addition to the family.