It's very clear I'm not welcome to live at home. What are my options? ?

Your mother is a piss of ****. Call the LGBT center and ask for help. Talk to your school counselor. Have you met any adult gay people? Reach out to the LGBT community and explain your situation. Is your city gay friendly? For instance dies your police dept have gay officers- if so they will be helpful. Ask the gay center fir welcoming churches. 🌆Also check out PFLAG.org- a wonderful support group.made up of mostly parents of LGBT kids. They will help. HUGS from a boomer lesbian. My heart goes out to you. Have you spoken to other members of your family? Please work on a plan quickly before your mother does something bad. 

Try pretending to be straight

Speak to the good in people and people will listen.  Try to understand your mother's position.  At the same time, remind her of her own motivation to be beautiful to you.

Others often forget their direction and may lash out at you in their insecurity or to pretend that they have some direction.

They don't profit from hurting you.

Sometimes you need to shame others into treating you better.

This addresses their own values and thoughts that they are good and beautiful.

If they still don't value you, they must value friendship, public opinion about themselves, or something else that you could show them that [being mean to you] would work against them.  

You need to point out how important and valuable the family is.  

A family is like a crew, a fighting-unit on a ship.

You ought to cling together the most when the seas are calm because there are dangers lurking below. 

We are living in a time of tribulation and people need to help each other to get along.

The family is the natural unit for helping and being charitable (or putting up with).

I think a family is simplicity of living - living the simple life.

You don't have to prove anything to them, they know your defects.

Nature provides animals with families as the easiest and most natural way to be.

Your family is familiar and you don't need to learn more about them, unless you want to. You don't have to talk, just being around is enough.

I'd suggest you re-calibrate your idea of what home life is supposed to be like.  To be entirely accurate, you ARE welcome to live at home, apparently.  Your mother hasn't thrown you out.  So you've got a roof over your head - which is a VERY BIG DEAL.  Yeah, you've been dealt a crappy hand, but don't overlook the good cards.  You've got heat, electricity, a bed where you can sleep without getting robbed or raped...you've got clothes and a way to clean them...it's unclear what the deal is with food but it sounds like you're eating.

Yeah, your mom is being mean to you and probably has incredibly ignorant ideas.  But don't forget she's only a small part of the picture.  You have a lot of really good things where you are right now - just a nasty mom that comes with them.  Take it from someone who ended up on the street as a young teen - you DON'T want to give up those things, even if they come with a bi tch attached.

Learn to be pleasant in your mom's face and ignore her ignorant jibes.  You've got a good deal, living in her house.  Try to continue to get away with that as long as you can.  Do well in school.  Save your money.  Don't get bogged-down in puppy love affairs or drug use...those are both attractive things that can totally wreck any chance you have of making a clean break when you're 18 and done with school.

Find a boyfriend that is privileged and has a lot of money! 

Choose someone you know and get a house by working a great job.

Contact your local gay and lesbian counselling service (they should be in the phone listings for your city or have a website) and discuss the matter with them as they will likely be able to give you some support and may even talk to your mother and make her understand it is not your fault you are gay.  They may even be able to arrange somewhere safe for you to live where you will be treated decently as likely your mother is breaching her parental duty of care with the neglect and anger she is displaying at the moment.  So many parents believe people just decide to be gay and don't realize you received a wrong Chromosome from them ( I think that Chromosome is supplied by the mother ) so in fact she was the reason you are gay.  You have a sexual disability and it's no one's fault but unfortunately your mother will likely always believe you chose to be gay.

Put away any cash you get.

On High-School Graduation day morning, pack your bags. So you can leave with your diploma in hand.

Maybe move & store your personal belongings early (day by day). Item by item with a friend.

OR

Report her to Social Services, Move to a Foster Home, or distant relative.

Maybe stop being gay and eat your mama’s cookin