Welcome to Susan's Place!
When I came out at sixteen, my parents said the same things to me, and they were wrong. I wasn't "too feminine" (what does that even mean? Are flamboyant, gay men too feminine to be men?), my desires were "all-consuming," and I did "show signs" as a kid. I just showed signs of being a flamboyant, nonbinary boy instead of a stereotypically masculine boy; I just didn't have the words or personal freedom to explore it.
Cisgender people can feel this weird, questioning back and forth too, but it's a lot less common. You could be a transgender man, you could be nonbinary, or you could be cisgender; what matters right now is what you want, and it sounds like you want to be a man. Which, for the average transgender person, is a sign that you're neurologically incongruent with your physical body, established identity, and/or outward presentation. It's not an all or nothing thing, though that's a common misunderstanding.
One of my earliest, clearest memories of wondering if I was transgender (though again, I didn't have the words) was stumbling upon a forum post about a "straight woman" who "wanted" to be a gay man. They wanted to transition, but they didn't know how, or if transitioning was even an option for them. It felt like a match had been lit in my brain, and I struggled to extinguish it. I was only twelve, and I still wonder what my life would have been like if I'd come out right then and there.
I don't know if breaking up with your ex-girlfriend was the right idea, but I also don't think your parents are right. Wanting to be a gay man, if you are a gay man (nonbinary or otherwise), isn't fetishizing gay masculinity. It's just. What gay men want. Just like straight men generally want to be straight, when questioned about it.
Regardless, I think talking to a gender therapist is your best, next step. Are there any LGBT organizations in your area? I met my first gender therapist, and first therapist in general, through an LGBT organization's counseling program. With any luck, they can help you sort out how you're feeling and how to proceed from there.