Hi welcome to YT and congrats on your new baby. I have a baby with very sensitive skin when it comes to topical products. Fergie with get blisters from certain shampoos. The only shampoo that hasn't bothered her is Mink Sheen.
MinkSheen Pet Shampoo -
It is a shampoo, conditioner, antibacterial agent and natural insect repellent. I'm not to crazy about the smell, but others love it.
I know you will find all the answers to your questions and more here on YT.