You definitely need an attorney familiar with immigration law, as your situation depends on numerous details. If you are a legal resident of the U.S., it might in the long run be better for you to go through the naturalization process.
Whether a person is a US citizen generally depends on the statute existing on the date on which the person claims US citizenship.
Under the current statute INA 320, an LPR child automatically becomes a US citizen when:
(1) At least one parent of the child is a citizen of the United States, whether by birth or naturalization.
(2) The child is under the age of eighteen years.
(3) The child is residing in the United States in the legal and physical custody of the citizen parent pursuant to a lawful admission for permanent residence.
If I remember correctly, back in 1997, the requirement is that BOTH parents have to be US citizens, unless one of the parents was dead or the parents were divorced.
A claim to US citizenship generally does not expire because merely because of passage of time. Thus, if you can prove that you were eligible to automatically acquire US citizenship in 1997, your claim should still be valid today regardless of the change in law.
You should consult an attorney who can get the relevant facts from you and look up the applicable statutes.