Which element exactly are you allergic to? I believe that some specific oils may cause the allergy in the soap, but it would be great if you indicated it before I advised you something. In general, I can advise you a firm
https://mildsoaps.com/, since they make soap without parabens, and because of this, you will definitely not have allergies. I like oatmeal soap, as I love its smell and like that it does not dry out my skin. So you can start with this model; I will be glad if you like it.