Cleansing recommendation perfect for dry itching

Does my skin turn red after cleansing because it is dry, or because I chose the wrong cleansing product? Since I have sensitive skin, I can't switch products once I try one and think it works well. I can't even do the cucumber face masks that everyone else does in the summer because I get hives.

I would appreciate it if anyone could recommend a cleansing product that is suitable for sensitive skin like mine.