If your child is truly having anxiety, counselling is really critical not only for her current situation but for her future. Anxious children become anxious adults and they need to be taught the skills to deal with their anxiety instead of letting it overwhelm them. Perhaps you can frame counselling in those terms, i.e. this is a person who will teach you skills to deal with your anxiety as opposed to someone that needs to fix something that is "wrong" with you.
That being said, it is obviously important to first have any purely somatic issues diagnosed and dealt with.
