OP, I went through something similar in Y12, though not to the extent it seems you are going through (currently in Y13). I understand you worry about talking to teachers, but I would highly recommend talking to/emailing your head of year/head of sixth form/pastoral team (whichever you are most comfortable with) about the difficulties you're facing in attending school. Realistically, you aren't going to get much help in getting back to school without them. Hopefully, they will be understanding and would be able to work something out with you, like reduced school hours or accommodations such as ear defenders/ANC headphones or sitting in specific areas of classrooms if there are issues with specific individuals in your classes or general paranoia (e.g. I struggled a lot with paranoia so had it organised that I sat at the back of the classroom in every lesson).
A-Levels are such a difficult time as it is, and going through them alone is daunting, but it is doable. Your school presumably has a pastoral team, I would recommend reaching out to them and seeing if there's anything specifically that they can do, such as giving you a pass to leave class if you get overwhelmed/need a break. Also, if you find this impacts your performance during exams, you can receive access arrangements such as rest breaks for mental health that can massively help.
As we're in the middle of Easter break, it may be easier to contact school now about receiving any accommodations that may help, so that when you return for summer term there is the slight reassurance of having those in place. The fact you are being excluded from communal areas (presumably not enforced by staff?) seems a clear case for bullying, which schools are obsessed with taking care of and so if nothing else you could take that angle to see if the school can tone things down. Obviously that is not a proper solution to the wider issue, but honestly it is a difficult situation to rectify, despite your innocence.
My approach in your shoes would be (assuming you cannot move schools whatsoever) to minimise contact with the rest of the sixth form as much as possible and have the strongest support network you can, whether through family or friends outside of school. By the time Y13 starts, people will have been away for 6 weeks and everyone will be much more focused on their studies, so the rumours and ****-talking should subside, making it a bit more manageable - some people may entirely disregard what's currently happening to you and be friendly by then! In such a small cohort, mob mentality is no surprise and when people are separate from the mob for 6 weeks, the strength of it weakens. If powering through summer term like this seems feasible, I would recommend it. Y13 is only 2 terms, after all! (this is what I did, and can say everything did very much die down this year)
However, if your family are close to/can afford one, there are also colleges that are designed specifically for people retaking years that I believe would accept you, despite you being 'too old'. I looked at some of these when I was in Y12 (note: I didn't end up retaking the year as my school was very accommodating) and found they were very appealing, though often they were exclusively online learning, which may appeal. Additionally, depending on the subjects you take, you may be able to transfer to another school for Y13 though I must admit it's rare for another local school to have identical courses to the ones you're currently studying (in terms of units, exam boards, etc).