I am not in NC but I can tell you the general rule. If you have a child who is of driving age or who will reach driving age during the term of the policy and the child is a resident of your household, you must insure the child. The insurance company, instead of adding the premium and child's name to the policy, could cancel you if it suspects you knowingly concealed the information about the child's age during the application process. In this case you probably told the agent about the child and the age of the child so they just added the coverage and raised the premium. This appears to me to be normal underwriting. The risk on the policy goes up when a child reaches driving age.
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If you got notice, you may be required to pay for the time the insurance was in effect. If not, then I do not see how you should be liable, especially, if you cancelled as soon as you found out. It may depend on both the policy language and the law in your state. You may want to contact your state insurance commissioner's office.