Could having acupuncture for a frozen shoulder give me back ache?

I do not think so: It is not supposed to because there different spots and if did hit the back spot it supposed to relief back pain if it was there.

Perhaps: For chronic medical problems there is often return of pain after a period of time - this usually decreases with number of treatment. If your shoulder was held in tightly and now has fuller range of motion - this will have an impact on back muscles which now have to adjust to the change of shoulder position. If that is the case it should be transient. That happened to me.