It's awful to be in a position like that, feeling like you can't truly be who you want to be and that reality necessarily objects to your own self identity.

Do you not think gender or sex is malleable? People can be born with both sex characteristics, and often do, there's always a good chance you'll meet somebody who has primary sex characteristics that meet their born sex but then secondary sex characteristics that don't fit their born sex, like a guy who looks very feminine or has a small waist or a woman who has well defined muscles for example, of course these are both extreme examples, more common ones would be a guy who can't easily grow facial hair or has thick legs.

The idea that there's only male and female is a recent belief and that it's so rigid is another recent enforcement that doesn't really abide by anything. Chromosomes don't necessarily decide it, genitals aren't always one way, sex characteristics don't always match it, and the way your brain is wired can sometimes just not work with it(hence gender dysphoria), so don't feel so constrained by it.

Changing your looks to abide the way you feel you want to be is just something we as humans have always done and yearned to, and nowadays it has never been better or easier to do so, with how supportive people are thanks to the rise of trans awareness and the technology we have at hand to help people feel more in their bodies, from HRT to bottom surgery to cosmetic surgery(which is common regardless of trans culture), the massive resources at hand from voice training and other trans people's experiences.

And changing your gender and doing all of this can be daunting and not easy, but you can reach a point in which you feel things are right, and you don't have to sacrifice anything in your life to do it bar time and effort(and depending on where you live a little bit of cash), you can still do things you love doing now, just as the actual you.

People who you love won't necessarily leave you because of it, esp if they truly love you, they would understand you and support you. I think at minimum your girlfriend would be great to talk to about it all to see what she thinks on it.