If you are just on a deferred finding, not probation, you have no duty to report new charges. In fact, you have a constitutional right not to reveal incriminating information to law enforcement. As for the new tickets, you can contest both. If you show up with proof that you were insured the judge should dismiss that ticket.
The only way Cullen Texas will find out about the ticket if the city of Houston reports to DPS that you got a speeding ticket. My advice is to hire an attorney who does mostly traffic tickets in the City of Houston and they will reset your case to a jury trial and the new court date will be anywhere from 3 to 6 months from now. Chances are that the city of Houston is not going to report an alleged speeding to DPS until you plea guilty or take a MANDATORY Defensive Driving. If you take a Mandatory Defensive driving then the City of Houston does report the speeding to DPS and then Cullen, Tx will find out because it will have the date of your offense when the City of Houston reports your defensive driving. There are ways around this but I would recommend you hire an attorney who does mostly traffic tickets and knows their way around the municipal court.
It is unlikely that the courts will communicate about your tickets. You have the right not to incriminate yourself, so if you say nothing there should be no reason why they would find out. However, if your deferral agreement requires that you sign an affidavit that you have not received any violation at the end of the deferral (yes, some courts do require this step), then you would be misrepresenting yourself to the court.
Nothing in this answer constitutes an agreement to represent you in any criminal case. Additionally, the information provided above does not constitute legal advice.