Maybe the oxidization will make it become into dioxins that then get stored within the biomass.
Nope, not what happens.
You do understand the body already deals with rusting metal already, right?
The hemaglobin in your blood, the oxygen carrying part of the red blood cell, uses iron as its main component.....and the iron decays over time.
So, if iron can be handled by the body, a little sliver of metal can, too.
Closer, but wrong too. Iron is an element, it doesn't break down. It combines with oxygen to form rust (iron oxide). Only some kind of isotope of iron would actually decompose. Hemoglobin contains iron oxide (that is why your blood cells are red (the red ones at least). The red blood cells get old and damaged and eventually get secreted and that is how you lose iron. Your body can deal with snickers bars too, shove one under your skin and see how well that turns out for ya.
A metal chip under the skin can
a) sit there and do nothing. effectively getting encapsulated and just hang out.
b) carry in some bugs and seed an infection
c) migrate around and possibly get involved with stuff like nerves, muscles, bones, blood vessels, or hopefully the surface of the skin and exit the body.
@OP That black puss you are seeing is probably some of the metal getting dissolved in the puss of the infection. You might be able to draw the metal to the surface with a powerful magnet taped to the wound while you sleep. Still you should get the wound flushed out by someone that knows wtf they are doing. You don't want to have a weird purple blister on your face for the rest of your life do you?