Oh, the poor baby. I think some of them have super-sensitive skin. One of mine did and the only detergent that worked was and still is ALL free and clear.
Cloth diapers didn't work for my sensitive skin little one, no matter the method I tried for washing.
I hope you find the answer, we just gave up and went with disposable.
(If you little one is super-sensitive, you may have to look at her baby soap, lotions, foods and even think all cotton clothing.)