Philosophy of Eowyn Sheildmaiden of Rohan

To understand the following piece I want you to understand that I am working off of one basic principle that you may or may not agree with. I believe men and women to be fundamentally different in who they are not just body function.
So I began looking at the different parts in The Return of the King that spoke of Eowyn Shieldmaiden of Rohan. Looking at the description of Eowyn when she is fighting the Lord of the Nazgul on pages 842-842, there appears to be some confusion as to her place in this battle. On one side you have being described in ways that say she is quiet capable, “Still she did not blench: maiden of the Rohirrim, child of kings, slender but as a steel-blade, fair yet terrible.”(Tolkien 842) Here it sounds completely natural for her to be in the battle fighting the Nazgul but not a page earlier you have Merry’s reaction to the fact that this was Eowyn on the battlefield. “She should not die, so fair, so desperate! At least she should not die alone, unaided.”(Tolkien 842) Looking at this, what stands out to me is that she shouldn’t be dyeing on this field because she is a beautiful woman.
Moving on to when Eowyn is in the house of healing she meets with Faramir, who upon first seeing her totally starts crushing on her. But she says to him “Shadow lies on me still. Look not to me for healing! I am a shieldmaiden and my hand is ungentle.”(Tolkien 961)
When Eowyn is “healed” she gives the following analysis:
“I stand in Minas Anor, the Tower of the Sun, she said, ‘and behold the shadow has departed! I will be a shieldmaiden no longer, nor vie with the great Riders, not take joy only in the songs of slaying. I will be a healer, and love all things that grow and are not barren.” (Tolkien 965)
This all implies that maybe she is not being completely happy being a shieldmaiden, or just a shieldmaiden. But can she be something else as well as a shieldmaiden? Can a woman be a mother, a lover and a wife if she “takes joy only in the songs of slaying”? Did Eowyn have to change to become the bride of Faramir or could she have become both? I think that this is a question that is bugging many girls from my generation. We are told we can be anything we want to be, but can we really be it all? Many believe that it is in a woman’s fundamental nature to be a care giver, and that the roles which females have traditionally filled have required it.
So is it ok for a woman to do man’s work? Or does that make her broken? None of the other characters in Lord of the Rings seem to need to be healed from being soldiers, just Eowyn. So is a woman to focus simply on loving, or can she be a fighter? That is the question I leave you with.