Welcome to HCM
Depending on the type of acne whether inflammatory or non-inflammatory, the treatments will be slightly different. Use of salicylic acid
cream is indicated for non-inflammatory type, but for the other type you could associate with doxycycline tablets for 1 month. Also, benzoyl peroxide
5% lotion twice daily + doxy is also a good treatment of choice for acne. Also use of topical steroids would also be good. You also need to know that, for your age group persistent acne
is normal and would give way gradually as you get older.
The other possibility for your rashes on the back is that you might not necessarily be suffering from back acne. There are always other possible skin affections to rule out when dealing with rashes ( papula or pustula lesions) for example prurigo, eczema/dermatitis, fungal skin infection
I will suggest at this point a visit to your doctor or a dermatologist
as I know you are worried because of the esthetic concerns the pose on you.
Hope this helps