First and foremost, make sure you are safe! Your physical safety is the most important thing!
If you doing anything to transition, even if its something as simple as cutting your hair or wearing male clothes means that you won't be, then I'd recommend you don't do so until you can move out on your own. Yes, I know its rough, but it'll happen soon enough.
If you can, get another binder for yourself. It sounds like you want to wear one, so as long as you do bind, do so safely! There are threads on this forum that explains how. Chest dysphoria is very common, so you're not alone. I'd recommend hiding the binder from your mother, especially since she threw out your last one.
Thrift stores are your friend! In order to find out what male size you are, if you can get to a thrift store, go look through the men's/boys clothes and find clothes that you like, and that fit you the way you want them to fit. Never mind your hips and chest, there are many tricks to hiding both if that's what you want. If you have the money, buy them and wear them. That might help your family get used to the idea...maybe. I wore jeans and t-shirts for most of my life, so my family was used to me continuing to do so when I transitioned.
If your hair's long, you can either get it cut short, have ti cut into a more masculine style or wear it in a man-style bun. Google "samurai man bun," there are many styles that come up.
If you can, see if your family will let you get into therapy. Even if its not specifically a gender therapist, it really helps to have someone to vent to about your problems. If you can't, talk to your grandmother or someone else you trust about how you feel, or write it down in a journal and hide it from everyone. It always feels better to let out your feelings, even if its only on paper.
I'm going to be honest. You have a hard road to travel should you decide to transition.
Sometimes, people expect a certain thing from you, and when you don't live up to it, they turn away. Family included. But it is your life. You are the one that has to live with yourself and your decisions.
But remember, this forum is here for you, just like others were here for us when we needed to vent, ask questions or simply be acknowledged.
And no, you don't need to have any kind of surgery to be transgender. Nor do you need to be on HRT. Its usually accepted that "anyone that questions their gender they were assigned at birth falls under the transgender umbrella."
Good luck little brother.
Ryuichi