My Mom refuses to take me to a therapist

I believe I have social anxiety disorder.
I haven't been professionally diagnosed, but I'm showing all of the symptoms. I don't ever talk to anyone in public or at school or at parties. I'm afraid people will judge me for the sound of my voice or for my accent (I'm a native russian speaker) or for my opinions. I never wear bright colors because I don't want to draw attention to myself. A few years ago when I was 10 or 11 (I'm 14 now), I was so anxious that I vomited from nausea every day before school. My parents knew about this but they basically ignored it. I don't vomit anymore, I have better control over my body, but I still get very nauseous before going into public.
and I'm sick of it. I'm sick of caring about what others think. I just want to be able to go out and have fun without worrying about anything. and I want to have friends. Even just one friend. One friend who I could open up to and who could support me. Is that really too much to ask for?
Anyway, I opened up to my mom about this a few months ago, and I asked if she could take me to therapy, but she refused. I didn't even bother talking about this to my Dad though, because I know he wouldn't understand. We're not that close anyway, and he always yells at me over small things. Last year he also basically humiliated me every day when dropping me off to school. He'd make me hug or kiss him before going into school, and then when I went out of the car he'd yell at me to tie my shoelace or something. All of this happened in front of a lot of fellow students. When I asked him why he did that he just said he was "building my character" whatever that means. But he wasn't building character. I think he was being downright emotionally abusive.
I also opened up about all this to my aunt, who I'm pretty close with, but she offered to take me to a christian therapist, so I told her no.
I don't really identify as a christian anymore (my family doesn't know that though), and I'd also like to open up to my therapist about being gay, and I highly doubt any christian therapists are lgbt+ friendly.
There's also some other weird stuff going on, I keep getting these crazy nightmares at night and I'm also paranoid all the time. I've also been getting violent intrusive thoughts.
So, I really want to see a therapist. I don't want to live like this.
But, If my parents won't take me, how can I go to a therapist? How can I get better?
Does anyone have advice?

Also, sorry for any misspellings or typos. I wrote this in a hurry.