It's a no-brainer. Relaxer=more damage and dryer hair. Simply swapping your Head n Shoulders for a non-sulfate shampoo=softer curls with definition. Then you can go from there (if you even need anything after you've been doing that for a few weeks).
As someone said, a relaxer will NOT reduce frizz necessarily. I can testify to that. Also, just leaving it on for 5 minutes is the equivalent to a "texturizer", still harsh on hair. In my "former life", when I texturized, it made my hair feel rough in places.