I started making soap because I had eczema. I learned it is what I leave out, rather than what I put in. Start simple, with one or two oil soaps with NO additives. Lard is a great place to start. If the person has had allergy testing (and if not, why not???), then you should have a list of oils to avoid. So avoid them. Remember, this is a trial and error process. Both on your learning curve, and them seeing if a soap is going to work for them or not. Leave at least 3 weeks of use on one soap before making a decision on whether it works for them or not. Maybe 6 weeks, because some times it takes a while before you react to something.
And you may or may not figure out if the soap is the culprit. It is more than likely something else, but at least you are minimizing soap adding to the problem.