You do need an external measure of your worth. Just make sure that what you use to measure yourself isn’t broken. Sorry for the lame analogy, but if you use the wrong tools to measure things, then you’ll get a distorted picture.
Judging from your thoughtful OP, you should be able to recognize that what your parents say about you isn’t true. They just say these things because they’re selfish and need to abuse others to make themselves feel better.
Two very common sources of criticism come from people who don’t know you or have a reason to make you feel bad. That’s ignorance and bias. If your father used the same logic to talk to you about global warming, you wouldn’t believe him, but when he says something that you fear might be true, you do.
What I would do is find external sources of opinion that actually know something about you and don’t have a reason to make you feel like shit. Your best bet is to find a good therapist. Beyond that I really have no clue. It looks like you’re not likely to move out of your place, so I would minimize contact with your parents as much as possible. Lie if you have to.
Oh, and self-esteem isn’t going to come to through external sources alone. You’ll have to actually accomplish something in order to feel good about yourself. I’m not saying you haven’t accomplished anything yet -just nothing that you feel good about. You’re going to have to find something that you admire doing, and then get good at it. It’s not like the movies where someone gets self-esteem first, and then gets good at everything else. Self-esteem comes after the hard work.
FWIW, you’re a really good writer, thoughtful, and you know how to open a story. There doesn’t seem to be anything wrong with you besides your insane family. Without a supporting family, even the best of us wouldn’t make it very far.
You’ve been hurt before and you’ve survived. You could probably manage this. You don’t really have a choice - you’ll have to ask them for help at some point. Might as well be before you get more traffic tickets.