Problems

[av1]

I haven't still told to my parents that I am trans. but now I am facing so many problems. First is that my mom is sharing with everyone my puberty-my father, aunts, grandmother, cousin, even with one of my friend and her mother. I don't think this is right even with someone non-trans. I can't even talk with all these people or my mother fearing they will start talking about this thing or may be tell them to others.  I am avoiding my mother on any conversation.
Second is that when I travel I will have to prove that I am the person on the ticket. Then they will ask me 'you are a girl?' At school I wait for my friends to tell the teacher when she says the same because I can't say yes as that is not the right answer. Why does everyone has to prove his/her gender? Why do everywhere people ask for knowing the gender, and that too they can't accept if I tell them the right one?

[Contravene]

I know some parents brag about their kids going through puberty because they like to marvel at how their children are growing up so your mom probably doesn't mean anything by it. Have you tried telling her that you're uncomfortable with what she's doing? If you haven't, that would probably be the best place to start. You could simply tell her that you would like to keep those things private and that you're uncomfortable when she shares it with others. Once you let her know that you need some privacy in those matters it might be easier to open up to her about being trans.

As far as the misgendering at school and other places goes, unfortunately it's probably something you'll just have to put up with for now until you decide to transition and can pass more easily as male. If you think your teachers will be understanding about your situation, you might be able to explain your discomfort to them. Also, if you're uncomfortable with things like being called a female name in front of the class you can probably request to only be called by your last name.