It's unlikely but certainly possible. I'm sure if you call a Tarrant County defense attorney, they can look it up for you and let you know what you've got out there and the status.
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I would call an attorney and have them look it up for you. There is always a chance that you may get arrested.
Depending on why you want it, and what form is has to be in, you can also purchase a subscription to an online service that runs background checks in order to get a copy of your criminal record. If you need an certified copy from the Department of Public Safety, you are right to be concerned that you will be arrested if you identify yourself to a law enforcement agent for that purpose. In Montgomery County, where I practice, many bail bondsmen will be happy to "check the system" for open warrants, and so will many criminal defense attorneys.
Katherine Shipman's response to your question is for general information purposes only. Nothing in this response should be taken as legal advice for any individual case or situation. This information is not intended to create, and receipt or viewing does not constitute, an attorney-client relationship.