Could I fix old citizenship papers for my mother?

There is not enough information here, but if your mother became a citizen when you were over 18, you would need to file for the citizenship separately. You might still qualify, you need to meet with an attorney.

It is not clear what goals you and your mother may have. If she was granted citizenship before you reached age 18, and at the time she was granted citizenship you already were a Lawful Permanent Resident (you already had a "Green Card"), then it is possible that you automatically became a U.S. citizen without any need to file a petition for naturalization. In that event you could file an application to receive a Certificate of Citizenship for proof of your U.S. citizenship status. You asked about amending the naturalization application that your mother filed years ago, but it is not clear what you had in mind. If she did not identify you as one of her children, it would be too late to do so now. Since you now are over age 21, if you have been a Permanent Resident for five years, you should be eligible to file your own application for naturalization. If your family had been represented by an immigration attorney when your mother filed an application in 2002, the type of omission you mentioned could have been avoided. At this point, the next step for you should be to engage an immigration attorney who, after learning all of the relevant details about you and about applications previously filed by your family, could advise you about eligibilities, options and strategies, including representing you in filing your own naturalization case. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.