tl;dr had/have BDD. Suffered an ED bc of it. In a better place now, but it's not worth your time
**im going to apologize right now for this giant block of text
I know exactly how you're feeling. Granted, my BDD is a hell of a lot better now than what it used to be, but I know just how bad it can get. Ever since I was in grade school and maintained my baby fat (and liked to eat a lot, but I played like 7 sports so whatever) I despised my body. I literally would look in the mirror and see a monster. Anytime at school and anytime with friends (esp around boys) my weight would be like 90% of my attention. I would constantly be stressing and thinking "omg I know I look even more monstrous from this angle" and obsessive things like that. In the shower I'd grab my fat and just want to cut it off.
Where my parents come in is that my mom is EXTREMELY food and body conscious--as in she obsesses abt food and has very low self esteem abt herself. She projected that onto me in my teen years (and occasionally now even though I've had blowouts with her abt it) where she'd have comments like "you're gonna wake up one day 500 pounds heavier [when I'm eating]" or "you'll never get a boyfriend with the way you eat" or we'd go shopping and she'd come in the dressing room with me and...just...the anxiety of having things not fit was horrible and she'd always just make noises or say things like "uh..oh" when zipping up clothes. Ugh
Trying to keep this as short as possible...anyways, in the summer before 8th grade, I was borderline anorexic..or just plain old anorexic probably and lost a bunch of weight. I was like 5'7'' and weight 110. People made comments and congratulated me, boys were into me, teachers became worried, blah blah. The things people said were great and everything and even my mom was proud but comments were still made from her whenever I'd eat like bread at a restaurant or something dumb like that.
In high school I gained a bit of weight back. My self esteem took a hit, and I decided borderline anorexia was just not going to work. I had heard of some distant friends who were bulimic and my other friend who wanted to lose weight decided to do it with me. Well my friend wasn't necessarily serious but I wanted to see if it'd work. Long story short again, what became an effort to lose weight the quick way, became a downward spiral of obsession and bulimia. Being depressed since I was around 12, my literal mind thought was: this is the only control I have in my life. This is the only thing I'm good at. So that became a good 4 years of self loathing and lying to literally everyone.
I'm in a better place now bc I know that caring abt my body this way is so toxic and not worth my time or thought space. It took time to get over it, but I just practiced being thankful to my body for keeping me alive and keeping me running even though I've treated it like shit! It's a constant struggle and I don't think it will ever "go away" but I try to find moments where it would be the last thing I'd ever think of! Your parents do not seem to understand how harmful and toxic they are being to you and your sister. If they can't see or even care to recognize how they're hurting you and your sister, then I would stop talking to them. It's harsh but maybe they will realize, or they'll ask why you're not talking to them and then you can simply re explain. My mom comes from the baby boomer generation where a lot of pressures were put on young girls and even my grandmas was like that to her; so I can't fully hate her for her ways. But I do confront her, and have fought with her on hve subject. Your parents need to get it through their brains... I don't know why they would want to make their children suffer.
Hang in there, pm if you wanna chat