Okay, Jsteam, I've decided to reply to this picture in this section, because this 'might' be the best place for it.
It is a specimen, to be sure, and a darn good question, too.

I'm replying on this picture because I think this one has more markings that can be perceived as "man-made" than the other one, but I don't think either one is a 'worked' artifact. And since you have been collecting Native American artifacts you know what I mean. There is always the possibility that they were 'curated'  or used by the NA for some personal purpose that could make them an artifact, but it would be more likely if they were found in context with other artifacts.
Just saying here and want to hear your reply, but they do not appear to be 'altered by man' to me. I'm guessing they're natural formations.
They look like old chunks of iron. The larger one that looks like an axehead or celt, has that raised rough exterior that does not appear to be chipped, ground, or smoothed at all. And this one has that weird spiral formation at the small end, but there is no sign of filing or smoothing in the grooves. This one also has some interesting marks along the upper right edge? You said it was hard enough that you can't make much progress with a file, and they are not magnetic?
Hematite is NOT naturally magnetic. Magnetite, which is an ore for iron and steel, IS naturally magnetic.
Iron Oxides, are not naturally magnetic, unless they are in combination with Magnetite.
So, my GUESS, is that these are Iron Oxide Concretions. They can be soft or hard as steel depending on their formation, and if they've been baking in a New Mexico sun!

Here's a link to a really good article about Iron Oxide Concretions. It is part of an article about Meteorites, which these concretions are often mistaken for.
https://sites.wustl.edu/meteoritesite/items/concretions/

Let me know what you think and anytime you want to go back and delete the posts of these that we aren't using, that would be great. Don't want folks thinking we're dissing you with an unanswered post!