It's not bank accounts you need to worried about, it's credir card accounts and loans that can accrue debt.
A fraud alert and "freeze" is a good idea if you think you have reason to think that your scoial security has been compromised. Please see the ID theft link below.
PLEASE READ THIS BEFORE YOU COMMENT, EMAIL ME OR PHONE ME. I'm only licensed in CA. This answer doesn't make me your lawyer, and neither do follow-up comments and/or emails and/or phone calls, and you shouldn't expect me to respond to your further questions if you haven't hired me. We need an actual agreement confirmed in writing before any attorney-client relationship is formed. This answer doesn't constitute legal advice, and shouldn't be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
Looking at your credit report was a great first step. Ensuring fraudulent banking accounts have not been opened using your personal identifying information is a great next step. ChexSystems provides consumer reports using information furnished from many financial institutions and would be a good resource. Visit https://www.consumerdebit.com/consumerinfo/us/en/chexsystems/report/index.htm.
Keep an eye on the credit reports. It can sometimes take some time before the trade line appears. If you get any more red flags (and never less than once per year), it should be addressed by reviewing your credit reports. For common signs of ID theft, visit http://www.ohioconsumerhelp.com/sub/id-theft.jsp.
Good luck to you!
NOTE: This Answer does not constitute legal advice. Every case is fact specific. To render a legal opinion, an attorney must engage in a consultation with a prospective client and review any pertinent documents. This communication does not create an attorney-client relationship with Attorney Amy L. Wells or WELLS LAW OFFICE, INC.