Very good points by the above posters. And I certainly agree with you about not wanting a short time fix. That is why specialmoms last question about ADD or sensory issues are so important. Both of those things can cause anxiety problems, and those problems will not go away unless the underlying problem is dealt with. Oh, and we do have AD/HD and sensory forums here if you need more information.
Hi there and welcome. I have a 10 year old that has anxiety from time to time as well. He's never had a panic attack though and I'm sure that has scared you and your son greatly. Panic attacks are NOT fun!!
I would consider working with a child psychologist (and would go private and use your insurance for it) to work on this. Just because you see a psychologist and acknowledge the medical condition that he has anxiety, it doesn't necessarily mean that you have to go straight to medication. There are good psychologists and bad ones and many child psychologist will work on coping skills for the anxiety without trying to initiate medication. Yes, some kids do need medication but don't let your opposition to it preclude you from seeking professional help.
Does your son have any other issues such as adhd, sensory, learning issues,?
It sounds as if you need to have your daughter evaluated by a mental health professional especially if mental health issues runs in the family. Also, it is very important that your daughter's are engaged in talk therapy. It sounds as if your 9 year old requires the skills to help her better cope with anxiety.
Psychotropic medication can be effective in reducing anxiety but therapy is the mechanism that will teach her coping skills. Meds cannot do this on their own.
The school counselor can be used as a resource for therapy services.