If your acne is severe, no over the counter (or prescription cleanser, for that matter) is going to help much. Have you been on / though about Accutane? It is usually the only "cure" for severe acne.
I used to struggle with back acne. I tried everything and everything. I started taking Minocycline a year ago and haven't had any breakouts on my back since. It was a miracle for me. My acne was moderate. It's said that head and shoulders works as well as dead sea salt but didn't work like I wanted it to. Good luck!