Your Child's US Citizenship is fine.

See the following at:

Naturalized U.S. Citizens: Proving Your Child’s Citizenship | LawHelp Minnesota (lawhelpmn.org)

When a parent becomes a citizen, are the children automatically citizens?

The child may be a U.S. citizen if ALL these things are, or were, true at the same time:

1. The child is under 18 years old.

2. The child is a legal permanent resident of the U.S. (has a green card)

3. At least one of the parents is a U.S. citizen by birth or naturalization. If that parent is the father but not married to the other parent, talk to an immigration lawyer.

4. The citizen parent is the biological parent of the child or has legally adopted the child. A step-parent relationship is not enough for derived citizenship. Talk to a lawyer if the citizenship is for an adopted child because there are special rules about this.

5. The citizen parent has shared or sole legal and physical custody of the child.

If these things are all true, your child automatically becomes a U.S. citizen in most cases. But you need to get proof of citizenship for the child. You can do this by getting a certificate of citizenship or a passport book or passport card.