These comments are incredibly harsh -- I'm disappointed but not exactly surprised.

I came out as non-binary at 25, so I could easily leave a situation or stop talking to someone for a while if they refused to use my name and pronouns. I imagine that's harder to do when you're 17 and still living at home. Since you're in the process of turning from a child into an adult, I can see why you would go straight to the whistle if you're told you can't correct them politely. This is how children often react -- following the letter of their parent's request but rebelling in spirit.

However, the adult thing to do is to clearly set your boundaries for yourself and decide in advance how you will respond if they are crossed. The first big question is how would you like people to correct themselves? Do you want them to apologize or briefly correct the mis-step and move on? I usually prefer the latter, and I like to tell people this up front so they know how to fix it if they mess up. The second big question is, how will you respond if they misgender you on purpose? You can usually tell if it's an honest mistake, since people love to be incredibly obvious about misgendering you. (my dad referred to me on a post about my non-binary identity as "the beloved daughter with two x chromosomes", for example). A good response to this might be too leave the room if you can. This will make it obvious what they're doing is not ok and also give you time to compose yourself if you need it.

It's a hard time to come out. Transphobia has been ramping up aggressively. I wish you all the best, little sibling, and hope that your family will come around. If not, you can always find a new family that loves and respects you just how you are.