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I'm not sure what you want me to say here.
In TX you are supposed to report all accidents. (see: https://myhoustoninjuryattorneys.com/wp-content/uploads/2014/10/How-to-Report-a-Car-Accident-in-Texas.pdf?d1914c), which you failed to do.
You can report it now, but reporting it will create your "permanent record" that you are worried about. (Not only do you have an accident in which you believe you were at fault, but you also left the scene of an accident without reporting it, and have no information for the other party).
I cannot advise you one way or the other what to do (we can provide "general legal information" but cannot provide formal legal advice or instruction - we do not have an attorney/client relationship).
Your options are:
It is unlikely that the other driver will return and claim greater damages - if they did they would have to prove the injuries/damages in order to prevail (plus, they failed to report the accident as well, the reporting obligation is on both drivers).
You would get a traffic citation, end up owing a fine, and get "points" on your driver's license.
Please keep in mind, this is general information only I couldn't tell you what exactly to expect (i.e. what citation/what fine/what points, or be able to confirm that this is the complete extent of the matter), I don't have all of your facts in front of me, and we are not permitted to provide formal advice (you will need to speak with a local attorney for that kind of advice). You can find local attorneys using the State and local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).