The fish-men representation was inspired by and in honor of the Abgal/Apkallu (Adapa, Oannes...) who were semi-divine. The ashipu were just human doctors that did have a priestly dimension, although very skilled in magical workings that were usually combined with the expertise of an asu, they combined several roles into a vocation that doesn't quite have an equivalent nowadays. Do you maybe aspire to be one some day?
SWP