The counsellor should be working to support your son and offer him a safe place to explore anything he needs to. Sometimes it’s easier talking to someone who isn’t family or a friend as there’s not that close connection. It’s good he’s getting support. Bullying can be an awful experience to go through. You sound like a lovely mum, OP. As others have posted, the counsellor won’t share their notes and they’d be unlikely to be useful to you in any case. I’m sorry that school isn’t helping in practical ways. No excuse now they have anti-bullying policies and ought to be using them.
The school offered counselling, which I really do appreciate. We asked for change of form class and to be fair they did that too. But other things we've requested just haven't been put in place. It's as if they're just hoping it will all just blow over.
Keep pursuing them through the anti-bullying policy. They should also have a complaints policy - start looking through that too. Counselling for bullying... I'm a big fan of counselling in general, but it's more important that the bullying stops, tbh. That should be the school's first priority.