Dryness after changing cleanser

I, while still using my last cleanser, got a dry spot with flakey skin, kind of excema-ish. Yesterday I switched to Cerave foaming cleaner, and it got crazy worse. I double cleanse with the ordinary oil cleanser at night. And now trying to restore my skin barrier (If that's what it is) I use the ordinary rosehip oil, and thicker moisturizers, but I'm breaking out like crazy. I know I have to give my skin time to heal and get use to it, but do any of you have any tips or advice on when to stop?