Just so you know, the farthest out teenagers can realistic see themselves is about 6 months out. Which is why everything seems much worse at that age, because you cannot imagine it changing.
Take a deep breathe and exhale slowly. Instead of focusing on your outside appearance or whether or not someone calls you by a specific name, try to find the good in things in your life. Don't hyper focus on what's going wrong. Try to focus on the things you are grateful for and the things that are going right. Gratitude and being miserable are such different feelings, they can't exist in the same space.
I'm sorry that your parents yelled instead of talking with you rationally. I think they are worried and don't know what to do to help you. It's not going to do you any good to call them names. Try to see things from their perspective for a bit, understanding both sides of the argument is crucial. So that you can both get where you want to go.
If it were me, I would try not to focus on the LGBT stuff for now, because odds are, in 6 months, you'll have different feelings about it. Focus on what's important, your future. Talk to your parents about how you are struggling in school and that you do much better when you have an in person instructor rather than virtual school. Putting things in their terms to help them understand. Like when a kid on here wants to convince their parents to spend crazy amounts of money on a hamster cage, we advise them to come up with a plan and a presentation. Maybe try to plan some goals about what you want to be when you grow up and what is the path to getting there. You will figure out who you are on the way.
If you are working, you have more freedom than you know. Save your money, so you have something to fall back on, and you can make your goals happen when you have the chance.
Ask yourself, what do I want in life (and not just in this minute) and how do I get there? A good counselor asks you these questions and lets you figure out the answer. There's no reason you can't ask yourself these questions.
You seem to be feeling very lost and confused right now, we all have those times when we are growing up. These moments will pass, you are a good, kind person, and I believe in my heart, that everything will work out. Your parents love you, even when they are not expressing it very well.
Feel free to PM me, if you just want someone to talk to.