I can understand how difficult it must be to have 2 children with mental health issues. You must be struggling too, trying to help both of them. With regards to your son.. he might benefit from first speaking to your GP and getting him some therapy of his own.. someone outside of the family that he can talk to freely without fear of upsetting anyone. He might also benefit from some time alone with yourself as it might seem to him that all your time is focused on your daughter (for obvious reasons) but he might be feeling a bit pushed aside.
As for your daughter.. having Aspergers can be very isolating (I speak from experience), especially at her age and she probably latches on to your son at school because he is a safe and familiar face when she is having anxiety attacks (i used to do the same with my own brother at high school). It might be worth finding a different type of therapy for her that is outside the "norm" as it sounds like your local primary care are fairly useless. When I was diagnosed, I was recommended to do Mindfulness therapy and I have found that this is a brilliant way to help control my thoughts, my actions and keep myself calm when I am panicking in public. You can either go to a therapist to learn it or you can get books and phone apps that can teach you. It might be worth giving it a try with your daughter and seeing if it makes her feel any more calm and less reliant on her brother for comfort at school.