I occasionally use sudocrem on my face, just a thin layer overnight. Works wonders for my skin and always notice the difference in the morning... Skin looks brighter, and skin tone evens out very nicely. Whenever I notice a slight stinging, with either sudocrem or a moisturiser, I know it's because my skin has dried out too much, which means inevitable micro tears in the skin, and now it's sensitive to the alcohol in the cream. This is not exactly harmful. Just uncomfortable. So a great product to protect the skin and assist it in returning to normal would be... sudocrem. That, and a few glasses of water!
If it stings when I apply a cream that normally doesn't sting, then I know my skin is struggling and needs some care. The last thing I'd do is wash it off with soap and water... Eek!