From a very personal standpoint, as someone who experience clear attraction to people across gender lines from a very young age, and who also never felt a fit with binary gender systems, it's harder for me to speak to some of what you're asking. That's because while I know a lot professionally about this, so I can certainly talk with you about some of it, personally, the whole hetero/homo setup never worked for me, and was never something that I felt ever could be a fit, even way back when when we didn't have language for nonbinary identities, so even back when I just identified myself as a woman.
So, if you ask me, in a personal way, I'd say that the whole framework of sexual identity which basically requires people have a binary gender -- in other words, to be heterosexual/heteroromantic, you are saying you are "one" gender and those you are attracted to are "the other", and to be homosexual/homoromantic, you are one and others are "the same" -- is really broken, and for those of us who aren't binary, it literally doesn't include us. From a professional standpoint, the same is true: that system basically requires people be on the binary.
Personally, I went with bisexual for a very long time when that's really the language that was available. I shifted to queer pretty much the literal second that framework was a thing I found out about, and I haven't looked back since. It does a good job, for me, of being a good general umbrella that really sums up all of this stuff about me: I'm queer in my orientation, I'm queer in my gender. Personally, I don't really need to say much more than that unless I'm speaking more specifically, in which case....well, I get more specific, which asks for many words, not just one or two.
Your mileage may vary, however. And some of that may be that even if it isn't a system that actually includes you -- or maybe it does, but you're still figuring that out -- something about hetero/homo resonates with you, so you still want to use them. You get to do that, if you want. You might also want to see how "queer" feels to you. As someone who is also queer, and with the given that YOU are the person who gets to decide how you identify, you sound pretty queer to me.
There's also an alternate framework for all of this you might not know about which centers the frame on who you are attracted to, without attaching it to YOUR gender in any way. That's this (which is included in this piece:
http://www.scarleteen.com/article/gende ... r_everyone ):
Androsexual, gynesexual, ambisexual or skoliosexual: These terms are a different framework for orientation than the framework of heterosexuality, homosexuality and bisexuality, one that can be more inclusive and expansive than hetero/homo/bi and doesn't require the gender of the person who is feeling the attraction to be defined in a given way, or at all. Androsexuality refers to someone who is attracted to masculinity, gynesexuality to femininity; am ambisexual is someone who can be attracted to both or either, or experiences gender as a non-issue, and a skolisexual, someone who is attracted to non-cisgender or non-binary people in general. Asexuality is also included in this framework. This framework doesn't make rigid asssumptions about the other person's gender, either: a person can be attracted to masculinity in women or femininity in men, for example.
Perhaps obviously, if you wanted to use that framework to talk about feelings you classify as romantic, you could use it for that, too (eg, "androromantic").
Just a couple more things (there's a lot in your post, so I am trying to cover it all, but also don't want to write a novel!):
• Usually nonbinary means, most generally, someone doesn't have to feel an attachment to the whole binary system of gender. That can mean someone feels neither masculine or feminine, like neither a woman or a man, but it can also mean that someone feels like one or both of those things, but doesn't experience them as a binary, or in the binary ways they are most often framed. Genderfluid is a term people who use it tend to use it to express that they do not feel connected to any one gender identity, but that they can or do fluidly move between more than one. You can be either nonbinary or genderfluid or you can be both.
• Your gender identity isn't about your partner. In other words, that your current partner is a heterosexual cisgender male only tells us things about him. That doesn't tell us about YOU, including because just because someone identifies themselves with those terms doesn't mean they only experience attraction to heterosexual cisgender women.
• No one "needs" sex, just for the record. Even those of us with high levels of desire. It's a want, not a need. Human touch is something that is an actual need, in that most people can actually get sick if they go completely without it, especially at vulnerable times of life, like infancy. But sex isn't ever a need. It's always a want, even when the want feels as strong as a need.
• What words you use for any of these parts of yourself are optional, including using them at all. You always have the option to just say you don't know or you don't have words for it if and when someone asks you to give words to your gender, sexual or romantic identity.