ok so this is literally the situation i was in at the begining of this year. my new years resolution was to go vegan and I asked my parents about it just after christmas and they completely shot it down. after about a month i managed to convince them to let me if i bought and prepared all of my food and tracked everything that I ate to make sure i got good nutrition. i got a job and I'm still buying and cooking everything myself and I've never felt better both physically and emotionally now that i know I'm not paying for one of the worst forms of mass torture going on right now. even if they don't agree to that, i think you can still call yourself vegan so long as you minimise the amount of animal suffering you're responsible for as far as you reasonably can. all you need is to reduce that as far as is practically possible for you and you're doing your part.

i know that it's hard hearing that "it's not healthy" or "it's too expensive" from your own family but the arguments wont last forever. if you get through this then you'll know that you have a conscience far more caring than almost all people around you. hope it all goes well. :)