What do you think about me being a closeted girly girl?
I'm not sure what to think about it. Can you explain more?
I hate to sing in front of people.
It's okay if you want to enjoy being girl in private.  However, you shouldn't feel like you are odd in any way just because you don't like to sing in public.  Most people do not like to perform in front of others.
Bitch, I know that's not the truth. All girls wanna sing in front of people and I don't. Singing is part of my feminine identity.
Singing in front of others can be uncomfortable for anyone, regardless of your gender. But if you enjoy being a girly girl in private that's okay, you aren't harming anyone by doing so.