If your child goes to school in Haikou, social security records are generally not required for local hukou, but I suggest you pay attention to the detailed rules of the enrollment plan published on the website of Haikou Education Bureau, and there will be requirements. Baidu search official website, Haikou Education Bureau, the website has the contact number of the Education Bureau.
Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.