I've had two csections getting ready for my 3rd. I'm the same way this pain killers. I hate them! I get loopy sick and just plain out of it. I nursed with my first two babies (will nurse 3rd), my dr knew I was going to nurse. I'm pretty sure they gave me Tylenol with codeine, it wasn't very strong. I never felt loopy. I alternated it with another non narcotic pain med. honestly I don't remember the meds exactly that I took. Take your pain meds in the hospital and during the 1st week home at least, not feeling pain you'll heal faster. After about a week or two I stopped taking the stronger med and just used the regular pain med. the pain wasn't that terrible best advice- get up and walk ASAP. You'll heal faster feel less pain.
It's only while in the hospital you are on morphine and that's just for the first few hours/day after that it's pills like Motrin and Lortab. I have had 2 and done perfectly fine. After the first day it's Lortab every so many hours and Motrin if needed. You will more than likely want it and need it for about a week or two depending on how you heal. It's perfectly fine to breastfeed too did with both and will again with this one in just under 7 weeks.
Let me preface by saying I've not had a csection- but I know a few women who didn't take their narcotic pain medicine for various reasons after a csection, and were able to manage with strong anti-inflammatories. So it may be possible to avoid the strong dopey pain meds altogether. You'll just have to see how your recovery goes.