The prosecutor may not offer evidence of you being merely arrested or issued a ticket.
This answer is based on the federal rules of evidence and depending on how similar they are to the Texas rules you may or may not prevail.
To address some additional concerns, let's delve into a segment on the rules and procedure in a courtroom. Your past criminal record and bad acts are generally inadmissible. The exception to this rule is if you decide to testify as a defendant. In that case, the prosecutor may decide to impeach your credibility by introducing evidence that you have committed crimes in the past: https://www.law.cornell.edu/rules/fre/rule_609
Since this is a traffic violation and we do not sentence traffic violators to significant terms in jail, the prosecutor cannot introduce any evidence about your criminal records at all, unless you open the door.
However, you have indicated you wanted to tell the jury that you have a clean driving record. The only way you can introduce this evidence, is to testify to it. You have to take the witness stand and tell the jury that you have never been convicted of driving violation. Because you want to take the stand in this case, you have to waive your privilege against self incrimination. Allowing you to only answer the question you want to answer would violate the concept of fundamental fairness in a court proceeding.
Now let's say you take the stand and testify that you have a spotless record. After you're done saying what you want to say, the prosecutor would get a chance to cross examine you. He could delve in to the specifics of your record. He could ask you about your driving course. He could ask about whether you had to take it. So on, and so forth.
Now assuming you have never plead guilty or no contest to a traffic violation. Nor were you ever convicted.
Rule 403 of the Federal Rules of Evidence states: "The court may exclude relevant evidence if its probative value is substantially outweighed by a danger of one or more of the following: unfair prejudice, confusing the issues, misleading the jury, undue delay, wasting time, or needlessly presenting cumulative evidence."
Rule 403 bars the admission of evidence which is substantially more prejudicial than it is probable. Evidence of simply being issued a ticket prejudices the jury against the defendant. As a society, we have a tendency to believe somebody committed a crime, even if they were not convicted. Ie. we say "he or she got off".
The jury will automatically think the defendant is guilty even though the defendant was never convicted. In the eyes of the law, if you were never convicted you are innocent. If evidence of being issued a summons were introduced it would inflame the passions of the jury and prevent the jury from rationally reaching a verdict.
For the aforementioned reasons the evidence of being issued a ticket, but no conviction is inadmissible.
Just a word of caution, trial court judges are given great latitude in their rulings on evidence. Additionally, if a trial judge rules this evidence admissible and you're convicted it is possible it could be construed as harmless error on appeal. Additionally, an appeal will most likely be more expensive than the fines you end up paying. Lastly, factor the possibility in the denial and weigh how critical a spotless record is for your defense.
My suggestion is to try to make a motion to suppress any mention of being issued a ticket and never being convicted in pretrial so the jury doesn't see you objecting to your record.
Disclaimer: I am not a lawyer. Contact a lawyer for legal advice and representation.