Pos Hep B Core Antibody

I recently had a hep panel drawn in preparation for an upcoming fight (boxing).  I came up positive for Hep B surface antibodies as well as Hep B core antibodies.  I am also in the medical field but not directly exposed to blood or body fluids and have had the hep b immunizations series. My question is there any potential for me to transmit hep B to another boxer if I get cut?  Or is that even a possibility?  Also, my antigens were negative but because I have positive core antibodies does this mean that my antigens will eventually turn positive?