By "my skin can fully turn into steel", do you mean exclusively your skin?

Skin isn't very thick and most of the sources I'm seeing wouldn't put it much thicker than 3mm at some of the thickest points with a generous definition of "skin". I'm seeing that you'd need about 13mm of steel to stop shots from most weaker handgun and rifle depending on many factors. Considering you'd need at least four times more steel than what you'd find exclusively on the soles of your feet to stop smaller/slower bullets I find it hard to believe that skin deep steel alone would make you completely bullet proof.

Supposing the steel did stop a bullet, though, the force from the impact is still going to hit you and likely cause some bruising to everything underneath the steel. Bulletproof vests slow bullets down before impact and distribute the load, but skill cause bruising. Raw, unshaped steel will offer no such benefits so you'll have the same (large) amount of force being applied to a smaller area on your body more suddenly.