Face wash is probably not going to cut it for back acne. I don't know if anything non-prescription is going to help much. If there is something, I have not found it.
I had back acne for several years during puberty v1.0. It was bad enough that my mother was freaking out about how I would 'never be able to wear a backless dress' (LOL, Mom, when did I ever express interest in wearing a dress?). Anyways, the acne was bad enough, but they left dark brown spots of hyperpigmentation. Thankfully, hyperpigmentation isn't actual scarring, though it does take a long time to go away.
I finally conceded to a dermatologist appointment, where I was prescribed TOPICAL Tretinoin 0.1%. I stress topical, because there is an oral form used in treating some forms of cancer which has a nasty list of side effects. About the worst the topical stuff will do, barring an allergic reaction, is over-dry your skin.
The Tretinoin cleared up my back acne and faded the brown spots significantly. My back stayed clear until I started taking T. I'm 26 months on T, and the back acne is not going away on its own, so I've started with the Tretinoin again. It has been a month, and my acne has calmed down a lot. If it goes like before, it'll be another six months before the brown spots have been visibly reduced. YMMV.
I would recommend seeing a dermatologist before you scar further.
