can someone please help me understand if this happens all the time by turning my skin black from wearing a steel printed jewelry
Probably the protective varnish coating has worn off, so that the metal can be attacked by moisture and skin oils. This will get you a mixture of browns and blacks from the various iron oxides, and greens and blues from the copper in the bronze - all of them harmless, but not looking nice. A new coat of clear varnish should solve the problem - probably nail varnish would do, as would any regular spray can.