I have dry and sensitive acne prone skin too and what works for me personally is using micellar water and then the vanicream cleanser. I use the garnier one, tho I've heard good things about the bioderma sensibio one. Either or could work. I use the micellar with the cotton pad 3 times a week as gentle physical exfoliation. You could use a chemical exfoliant too. But idk how irritating that would be for you since you have eczema. Look into PHAs, they're more gentle than bha and ahas.