You'd have to impart carbon into the melted down iron to turn it into anything that can technically be called steel. And it requires a completely different forge from the one you likely have.
Which is a *** of a process and at the end of it, a lot of the material you're going to walk away with is going to be pretty mild steel.
Many, different types of "steel" exist, with just about as many ways to forge it. Adding carbon to iron is as simple as adding charcoal, making charcoal is not hard (it is a byproduct of the forge). Yes, it would be a primitive steel, like I said and it has been around for a few thousand years.
A pure iron sword is the cheapest, quickest, and primitively made sword. Simply because the base iron ore is just quickly melted down and pounded into a blade. The more time put into it and the more the iron is worked (heated in the forge and folded) the stronger the metal becomes. Which is what I basically said in my first post.
My forge is built from field stone at the base of a hill with a billow on the bottom. Was something i just tossed together to see if it was going to work. It gets pretty hot, but working the billow is a pain in the ***.