Hi C.---I'd like to suggest another idea. Look at your diet to help with this problem. First, be sure that you are eating mostly plants; fruits, veggies, whole grains, legumes/beans, nuts and seeds. Then, eat more of those that have a high content of omega 3 fatty acids. Those would be ground flax (a HUGE superfood-fiber, protein, omega 3's, vitamins, minerals and cancer fighting properties), walnuts, pumkin seeds and soy and canola oils (these are usually GMO if not organic). Of course, cold water fish will also provide omega 3's, but TOO MUCH animal protein is not good for long term health. Increasing your omega 3's should, in time, help your skin to withstand the frequent assaults AND heal faster when your skin is irritated.
Plants contain the nutrients necessary for your body to both protect and heal from the frequent had washing and skin cracking. Even if you feel that you eat alot of fruits and veggies, it may not be enough for your body. I truly believe that our food does not contain the nutrients today that are necessary for disease prevention. There are many reasons for that and, if you'd like, we can continue that discussion later. But, I believe that's why major health organizations are recommending that we eat 10+ servings a day...and more if you exercise or are experiencing any health conditions.
So, I know it may seem pretty out there, but I am confident that improving the diet could help. Understand that I am not suggesting your diet is poor, just that it may not be good enough to overcome your skin sensitivities. I am learning about the healing powers of food in a series of wellness classes, taught by a Naturopath who has her PhD in Nutrition. I would be happy to share details of what she teaches to support my suggestions. Feel free to contact me at any time. Take care and good luck with your quest. Be well, D.