I empathise with you. Although personally I went to a state school where they'd be thrilled with your grades, I did have some teachers who treated me or my friends like this. One girl got an A in a practice coursework essay and the teacher had a go at her in front of everyone and made he re-do it even though she was happy and many others in the class got less than that.
The main thing to remember is that if YOU are happy with your grades and the people that matter most to you are supportive (family and close friends) then you have nothing to worry about. I got very fed up at school of people saying 'you can do better' and being disappointed with a good result because they were expecting higher. It makes you feel rubbish when you haven't done anything wrong.
Try and stay positive and keep reminding yourself of how you're happy with your grades.
Plus bear in mind that you are only in year 10, you have a whole year before your final GCSE exams and most people, in my experience, improve results dramatically from their mocks in January before their exams, let alone in an entire year. This is one problem with a modular approach to GCSE. So it is likely that you will get higher anyway.
The entry grades for sixth form will depend on the specific school so you would have to look into that, on their website or ask sixth form staff. For example, my sixth form only required 5 C's or above, and a B in maths if you were doing that subject, and even then they were lax on those requirements. It might be worth looking at other sixth forms in the area though if you are unhappy there. If they are pressuring you too much it could be bad for you. You'll have to weigh up the pros and cons between going somewhere you'll be happier and could still quite easily do well maybe even better and going to a grammar school which could make it easier for you to get good grades.
Personally I think your grades are good and you have nothing to worry about, I would be very happy with them. I know it's a while away yet but were you considering uni? If so what sort of uni's were you aiming for? Cause those grades wouldn't hinder me at all at any of the unis I looked at, general average unis would think them good.