Dry skin and eczema often comes together. I have inherited dry skin from my late mother whom I remembered had scaly and peeling dry skin on her legs during her later years. I too I noticed had scaly and peeling skin, not only on my legs, but on my face as well.
In addition, I suffered from extensive eczema on my back many years ago. When I was in San Jose, California, because of the dry air, I noticed my leg itching and peeling skin on my legs the next day after arrival.
Using Oilatum soap recommended by a Dermatologist (skin doctor) didn't help much. So how did I solved my dry skin and eczema problems? Simple. I just stopped using soap (except for washing hands and also when using soap is unavoidable which is not often). I just used plain water for bathing.
Did bathing with plain water caused any problems such as body odour? Nope, as far as my observations went. None of my family complained of body odour. Neither did my friends complain of body odor when we gather together. I never notice people moving away when I am forced to be near them such as passengers on public transport or private cars.
I am still monitoring this simple plain water for bathing remedy for dry skin and eczema and will report further developments in due course.