Johnson &Johnson makes a cleanser that is soap free. Its call Purpose. It comes in a bar or the pump and its not that costly. about $4 for the bar, and about $6 for the liquid pump. Its great, and it doesnt dry out the skin! Good luck
Have you try "Pond's" Clean Sweep? It is cleansing and makeup removing towelettes. I am very sensitive to soap and some make up remover. I can't handle Olay's products, I break out. I used Pond's Clean Sweep and it is the only product that I can handle without reaction.