Found It!
Okay, so I'd been having difficulty figuring out just what to call this, since I'm physically nonhuman in the sense that I have some nonhuman traits that might be physical, but not in the sense that I have nonhuman DNA or a body. And I've been searching for a way to refer to it - psychologically human doesn't ring quite right, nor does physiologically.
While reading a post I realized that the difference between me and other nonhumans is that I actually perceive myself as physically human still, with no conflict between the human and animal sides. And I discovered adhuman might be a good way to refer to those differences. Adhuman would denote someone who is human but in more of a mutant sense, where you're physically human but also other in a biological, known way.
As I was searching my term I would find abhuman, a term denoting any separation from normal human existence, like a mutant, werewolf or vampire. Abhuman is a science fiction term, but it's also used to refer to the humans in the Warhammer 40,000 universe, and I don't know if I wanna go there and get confused for them... So adhuman might be a better term for me.
I'll have to see whether adhuman or abhuman works better for me (abhuman denotes a divergence from humanity while adhuman would denote an addition to it) but yes, this might be what I am.