I have a speeding ticket that I haven't paid for yet and it may be a warrant and I also have a ticket I put on payment plan but I didn't pay the last payment and it may also be in warrant status by now
You can be and will likely be arrested on the spot. If you had a payment plan and defaulted, and a warrant was issued, then you would be the proud recipient of a Capias--warrant issued by the prosecutor. If you walk in without having addressed them first, Expect that they will arrest you at that point.
Personal Injury Lawyer
I would think this is a definite possibility, but I am a California attorney & not knowledgeable with TX laws. You should immediately consult a local TX attorney before you do anything further - call an attorney ASAP
This is not intended to be legal advise or as legal representation. I am a California personal injury attorney . Be aware that every state has its own statute of limitations; and statutes & case laws that govern the handling of these matters.