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Unfortunately yes, I do think it was a violation of the child's privacy rights. At this point I do not know if they will file a complaint but you should probably discuss it with the child's parents.
I did some additional research for you. While your child care center is probably not a covered entity under federal law, the therapist you have for the child likely brings you under the definition. Also, there is a Texas Medical Privacy Act that applies to any institution that maintains health information.
Let me know if you have any additional questions otherwise a positive rating would be greatly appreciated.