Unfortunately it sounds like you were the victim of identity theft. Traditionally identity theft refers to your tax returns or other financial accounts being stolen or meddled with, but it can also include situations like yours where someone gives your name and identifying information to police officers.
My recommendation would be to file an identity theft report, and to have a copy of that report with you when you go into job interviews or make job applications so that you can preemptively explain the situation to employers and provide them with some solid evidence that you were a victim of identity theft. Identity theft happens, so hopefully with a report in your hands, employers will be more understanding.
In order to file an identity theft report, here's what you'll need to do:
"1. Submit a complaint about the theft to the FTC. When you finish writing all the details, print a copy of the report. It will print as an Identity Theft Affidavit.
2. File a police report about the identity theft, and get a copy of the police report or the report number. Bring your FTC Identity Theft Affidavit when you file a police report.
3. Attach your FTC Identity Theft Affidavit to your police report to make an Identity Theft Report."
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