You may want to experiment with your own soap for sensitive skin. You can purchase your essential oils here, or from any other reputable supplier. At Hopi we use only olive oil to make our soap base, but you may want to try coconut oil, castor oil, even cooking oil. These pages have links to pages that talk about the different properties of many oils and how to work out the proportions of lye to oil you will need to make your soap.
Once you have developed a recipe of your own, make sure you have the safety equipment you need. Lye burns deeply if it comes and in contact with skin and clothes. At a minimum you will need a set of overalls, shoes that cover your toes (I use gumboots), thick gloves (not the see-through medical kind), eye glasses or goggles, to work in a well-ventilated area (or outside) and have direct access to a fully functioning sink. I make sure the children are out of the house (e.g. at daycare or at school - NOT taking a nap) and turn my phone off. There are many other tips on the links given in these pages.