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It definitely is possible that you are androgynous!

As far as your hair goes, a hairdresser may be able to do something with your hair even though you have stress pulled. Is it worth going to see one to see what they say?

You may also be able to purchase something known as a binder, which is a device that is used to safely reduce the appearance of breasts. Be sure you follow directions, such as how long you should wear it, not exercising with it, and don't get too small of a size that may restrict your breathing and cause damage.

Maybe you can start experimenting with a different name with accepting friends or family members. It's okay if you don't want to do that, but it can help you to see if you find a name that "fits" you more and makes you feel more comfortable. It's also okay if you change that name a few times, because it's all about seeing what makes you the most comfortable.

I've had something similar happen to me when I came out to my parents. I thought I was a lesbian at the time, although now I know that this isn't the label for me. My mom asked me who else is a lesbian that is making me think that I am as well. It's a good start that they're pretty accepting, but I'm sorry that they make jokes about your sexual orientation. If that's something you're uncomfortable with, maybe you can tell them "I feel uncomfortable when jokes are made about my sexual orientation. In the future, I'd like this to be off-topic."

If you tell them about your gender identity, maybe you can write it in the form of a letter that you either read to them or give them to read. That way, everything is gotten out without interruptions or nerves getting in the way. Make sure that coming out is safe for you before you come out. You can also tell them verbally. If you do this, I'd do it on a day when they are in a relatively good mood so they're more receptive to what you have to say.

I hope this helped at least a little!