Order credit reports from all of the three major credit reporting agencies. You are entitled to one free report each calendar year by federal law, so take advantage of that law and get your credit reports.
Contact each of the three credit reporting agencies to ask that a credit freeze be put on your account. Do not settle for a fraud alert, because credit card issuers are able to ignore a fraud alert if they so choose. A credit freeze is protected under federal law and requires any creditor to confirm your identity with you prior to opening any new accounts. You can do a credit freeze over the phone with Equifax and Trans Union, but you will need to either go online or mail in your information to Experian.
Make detailed notes when you speak with the credit reporting agencies and keep these notes, along with any correspondence you receive from the agencies, in an expandable file folder for safe keeping.
Using the credit card bills for each of the unauthorized credit accounts, contact the police and file a complaint for credit card fraud. This will help you in two ways. A police report will help you to prove that a crime was committed using your personal information but not by you. This will help you talk to the card issuing companies when you dispute the charges, and it will allow you to prove to the U.S. Social Security Administration that your identity was stolen.
Contact the companies that issued the unauthorized cards and dispute the charges.