Let me know what area you live in or want to live in. If you know the elementary school that your student is going to now, I can work from there.\
There are many private schools in Dallas and D magazine publishes a guide to private schools. You can look that up at D magazine.
My grandchildren go to private schools in Dallas, so I can provide some first hand experience and recommendations.
I am happy to help. Feel free to contact me. The link to D magazine is shown below.