I want to be put on homeschool but my parents wont allow it?

[Anonymous Questions]

I have really bad anxiety around people. I saw a psychologist and she said I have social anxiety disorder, but I never saw her again because she was pretty rude to me. I like to learn things, but I just don't like being at school. I do everything I can to keep my anxiety calm but it just happens. I'll have these major panic attacks during class usually once everyday, sometimes more than once where I'll feel like I can't breath because my heart is beating so fast and my chest burns to breathe. It usually last just a couple minutes and I try to keep as calm as I can, but when everything is all done I don't feel normal. I feel really dizzy and I sort of feel like I'm in a dream, like I'm just on auto-pilot and I'm not aware of everything that's going on. It's not a pleasant feeling. People at school are just mean to me, not for any real reason because I haven't done anything to them... just because they can because I don't say anything to them or acknowledge it because I don't want to deal with it. A lot of people have brought it to my attention that I have really shaky hands, I can be perfectly calm and my hands have sort of a tremor. I don't drink caffeine or sodas or anything on a regular basis, I prefer water... sometimes different types of teas. I really don't like going to break period or lunch period at school because I don't know what to do with myself. Sometimes when I'm at school I have major thoughts about suicide. I don't think I would ever do such a thing but I think about it a lot at school, I haven't told anyone because I don't want them to worry about me. Most of my classes are UP/AP harder classes and I have to ride the bus home. When I get home I have about 4 hours to get a load of homework done. When I get home I'm basically wiped out from just being at school and all I want to do is sit around on my bed, sleep, and sometimes cry; I'm a train wreck. I wanted to go on homeschool because I felt it'd be more comfortable for me (I know it's sort of selfish) and I figured that if I worked harder and did it over the summer I'd be able to finish school earlier.
Before anyone tells me to see a doctor and get medication for this, my parents are really against medications. I don't think they understand how I feel. They say medication is totally unnecessary and it was something that was between me and myself.
How can I convince my parents to let me go on homeschool?