My 9-year-old daughter has social anxiety. I want to treat her without medication. What are my options?
Yes. You should start perhaps by seeing a child psychologist and behavioral pediatrician who may be able to come to a more structured diagnosis and suggest options if needed. This may simply be a variation of normal behavior and social skills.
See this link for a perspective on your question:
https://socialphobia.org/social-anxiety-disorder-definition-symptoms-treatment-therapy-medications-insight-prognosis