I have really bad eczema too, and I use Aveeno body wash, in the unscented kind (that probably has sulphates in it, but it's really gentle to me)
I'm mostly a 3b-c, with a bit of everything else thrown in.
I'm 17 years old.
SL when dry.
I'm kind of CG (occasional sulphate)

Wash: Miss Jessie's Creme de la Curl Cleansing Creme, Kenra Moisturizing Conditioner, Occasional LowPoo grabbed from a drugstore or Biotera Moisturizing Shampoo (for BAD buildup)
Condition: Kenra, AOHR, Queen Helene's Cholesterol, Biolage Conditioning Balm, Generic KPak
ALWAYS Biotera Styling Gel
Haven't found a leave-in I like yet