You didn't screw up! :) There could be lots of reasons why your baby has rashes. You want to worry less about product and more about the diapers you are using and how you are using them. Babies don't need to have any chemicals or products on them and it isn't healthy for them when you put it on all of the time.
There are lots of possible reasons for peeling. Some babies have sensitive skin and can get chemical burns by chemicals in the diaper such as absorbent chemicals, plastic, perfumes, dyes or the chemicals used to bleach the paper. Some babies are sensitive to their own urine, so they have to have their diapers changed immediately after they pee instead of sitting in a wet diaper until it gets full. Some babies' skin needs lots of air and sitting in a diaper can cause rashes. There are so many reasons.
One or more of these might help:
1. Try different brands of diapers until you find something that doesn't cause a reaction.
2. Be sure to change your baby's diaper immediately each time she pees.
3. Switch to cloth diapers (I highly suggest Kawaii baby bamboo minkie/minky diapers, they are my fave!), especially cotton or bamboo.
4. Try elimination communication.
My babies have never once had a diaper rash, but I don't know for sure why that is. It could be because I keep them in dry cloth diapers and don't let them sit in pee. It could be because we do elimination communication, so they almost never pee or poop themselves. Or it could just be luck or genetics.