Keep hydrated and Lanolin(sp) cream is good for dry skin. not sure which if either are better for stretch marks since i didnt use anything for mine. Aloe would also be safe for treating dry skin. I used aveeno face wash during pregnancy. I would wash face while in shower.
I just use a clean and clear exfoliated face wash that helps get the dry flaky patches off my face then use cetaphil for after. That's weird that it is burning. Maybe talk to your doctor because I don't think that is normal for cetaphil a non-sented recommended face lotion to burn like that.