Child psychologist in Helsinki area and private health insurance coverage

Hi
Is there any good child psychologist in Helsinki area. My daughter who is about 8 years old is suffering from anxiety.
She is having vomiting and nausea feeling regularly especially after eating something and in intervals. There are weeks when she is okay but in last 1-2 years she is regularly having vomiting feeling. Initially we thought this is about gluten allergy but with or without gluten free diet she is having same symptoms and tests are also clear.
I strongly feel that she is having anxiety because of her behavior.

So i am looking for some child physiologist and also would like to hear if child physiologist really help. Do small children of this age open up to them.

Another thing does private health insurance cover for such visits. And which private health insurance you recommend.