If you're working hard to get 3 x A*'s to study maths at Cambridge - then I would say that that's an indication that your mental health is in a good state.
That type of dedication for worthwhile ambition is to be commended.
The comments from your peers are just childish jealousy from those unwilling to put the effort in to get to Cambridge, or unable to, due to a lack of academic ability, even if they worked twice as hard as you. Take their jibes as a massive compliment that you are doing the right thing with your time now. And also that you are significantly more mature than they are.
I bet your teachers don't knock you for your attitude to getting into the joint best university in the world. They have far more sense and wisdom than the kids in your year.
Getting questions wrong is a great way to learn. Never have any fear in giving an answer in school or uni. It's not about whether your answer in class is right or wrong. It's whether your answer in the exam is right or wrong that counts. And then once you've graduated, it's your ability to do whatever job that you decide to do that counts. Having the confidence to speak up, even though what you say might be wrong, is a good asset for most jobs.
Analyst89 has given sound advice on seeing your GP and taking things from there. I'd recommend you follow Analyst89's advice.
Studying for A levels - especially to Cambridge standards - is the most demanding academic thing you will ever do. Get past this hurdle and studying for exams gets easier and more enjoyable once you're at uni.