If the tickets were from DPS or a county agency, check with the Clerk of the court where you were supposed to appear.
If the tickets were from a city agency, call the municipal court of the city where the citation was issued.
Many Texas cities are also now part of program where your Drivers License will be suspended for failing to take care of traffic citations. Driving While License Invalid is a Class B Misdemeanor, punishable by up to 6 months in jail and a $2,000 fine. Do yourself a favor and take care of this before you get yourself into bigger trouble. Most courts will allow generous payment plans and will continuously adjust payment schedules to your needs, but you have to contact them before you get arrested.
Of course, you can always turn yourself in and get "Jail Credit" for time served, which I think is now set at a minimum of $100 per day for the state. Around here, saavy traffic scofflaws used to turn themselves in just before midnight, spend a night in jail, get magistrated at 7 in the morning, and get $200 credit towards their fines.