Yes it is possible the city reports your citations to a statewide database that the state has when you renew your driver license.
Good luck to you.
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If your city tickets have gone to warrant, you can be arrested on the spot at the DPS office.
If you do not have a driver's licens, then you will not have a driving record. However, if you owe money based upon the identifying information you use to obtain an identification card and you have a capias pro fine, then you may be arrested at the DPS office. If you have paid your fines and just want to get an identification card, you will not receive any "points" against your identification card.