Can the acne on my back be caused by my night sweats?

No, but...: I am more concerned about why you are having night sweats in the first place; this is something you will want to talk about with your physician. If the acne is in fact miliaria (a different skin disease that may feature little putules), this is caused by dampness, and acne can get slightly worse on such skin. Today's rx's can handle almost all acne -- again, your physician can help.