It is very important to sleep on your back after any breast surgery. You need to protect the surgical site, and the healing incisions. Any pressure, shear force, tension force, or excessive movement can lead to complications including bleeding (hematoma), wound separation, delayed healing, and other potential cosmetic issues. After the investment in surgery and desires for an optimal outcome, it is critically important to strictly follow all post-operative instructions so everything heals properly without complications.
I think that you should follow your surgeon's advice. I let patients sleep in whatever position that they feel comfortable.