Infected eczema

Fizaflowery
My babies face and head are infected because of eczema, he has been on antibiotics and has a steroid cream, but because he doesn't stop scratching the infection keeps returning, I was wondering if a couple of drops of dettol liquid can be added to his bath to stop infection and to help it, I am going to ask the doctor, but I was wondering if anybody had tried it and did it dry out the babies skin even further?