Short answer, no. Europe's iron was nothing special compared to what was being used in other parts of the world.

I specialize in early medieval iron working, and can't speak with as much authority about the later middle ages. But here's what I can say with certainty:

The Roman Empire made a ton of iron (so much that you can still observe the layers of pollution from iron smelting in core samples from Greenland's glaciers). But Western Europe's iron production slackened off after the collapse of Rome's military industrial system. There are sites in Scandinavia that produced tons of iron, and others in Eastern Europe, but not on the pre-medieval Roman scale. And the iron they produced was very inconsistent in quality, with the result that early medieval weapons were often rather soft, dulling and deforming easily.

This improved over the next several centuries, and you see more steel being used in place of phosphoric iron (which is hard but brittle, unlike properly hardened and tempered steel). But through the Viking Age, weapons are still very hit-and-miss in quality, and while Europe made enough iron to meet its basic needs, you don't see much of a surplus.

Early medieval iron was scarce enough that controlling the limited sites where it was produced allowed some local elites to establish themselves as local power brokers. One of the royal palaces in Kent (England), which was just excavated over the past three years, had an iron factory within about 10 meters of the end of the king's feasting hall. So iron was important, and hard enough to get that conteolling its production was a big deal.

Much better steel was being produced in parts of east Asia during this period (though there's scant evidence much or any of it made it back to Europe). I know much less about Asian iron production though, I'm afraid.

Technology did improve, with the introduction of new furnace technology toward the end of the middle ages. This technology (like the blast furnace, for making cast iron) had existed for centuries in Asia before arriving in Europe, however.

Regarding recycling: some early medieval weapons were made from recycled iron, and it must have been common to make other, less important objects from recycled metal. Rome left tons of iron behind in ruined buildings, and we have clear cases where we can see that this iron was scavenged. Medieval wrought iron is high in silica (as a byproduct of the bloomery smelting process theough which ore was turned into metal), which makes it very easy to forge weld; it was simple for early medieval smiths to weld scrap together just by heating it hot enough and hammering it together (which is clearly how some of the weapons I study were manufactured). In at least one case, I can point to a broken weapon being recycled into a new weapon.

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R.F. Tylecote, The Early history of metallurgy in Europe (1987) is a good overview of European metalworking (including a lot of information on iron in the middle ages).

R. Pleiner's books on Smelting (2000) and Blacksmiths (2006) also give excellent overviews of the evidence for ironworking in Europe (both prehistoric and medieval). They're exhaustive and encyclopedic, in a good way.

Tylecote and Gilmour, The metallography of early ferrous edge tools and edged weapons (1986) is a great study of the quality (or often, lack of quality!) of many prehistoric, Roman, and medieval iron tools and weapons.

And for a great study of recycling in early medieval Britain, see this article (which you can read for free): https://www.academia.edu/2065623/_Recycling_in_Britain_after_the_Fall_of_Romes_Metal_Economy_Past_and_Present_217_2012_3_45

I could point you toward more resources if you're interested! Several PhD students at Bradford have recently completed excellent dissertations on medieval iron. They're very technical, but very rewarding to read if you're interested in the material science of medieval metal.