Cold sores are caused by herpes simplex type 1 infection. As a viral infection, unless this has totally healed you may still likely transmit the infection through direct skin to skin contact. Wait for the sore to completely heal. Any cut on the surface of the skin may aid in transmitting the virus. This should resolve on its own. Getting enough rest, eating well, drinking plenty of water among other things will be able to help.
It is necessary to note though that HSV infection usually stays within the body .HSV infection especially type 2 may be shed by the body even after treatment.