M.A.
My experience is that Dr. Bronner's can be very drying. Are you using the liquid castille soap? You know, the regular stuff? If so, I would discontinue that immediately. As an adult, I can't use it on my skin undiluted, so I imagine it's the same with a child.
There are a couple of alternative options, though. You can add a few drops of tea tree oil to any shampoo. Or you can use the Dr. Bronners that you already have to make your own shampoo. 1/3 C Dr Bronners, 1/2 C coconut milk (like from a can), 1 tsp olive oil, 10 drops essential oil of your choice. Combine and shake. Shake well before using and use about a quarter-sized amount. Makes a great shampoo. Although if you already have the tea tree oil Dr. Bronner's, you could skip the essential oil altogether.
Hope this helps.