According to the Texas Highway Patrol, TX law requires every person sitting in the front seat of a vehicle to be secured by a safety belt. The law also states that all children under 17 years old must be secured with a safety belt or in a child safety seat, whether they are sitting in the front or back seat. A child less than four years old or less than 36 inches tall must be secured in a child safety seat.
Drivers can be stopped and ticketed for a safety belt violation if any of their passengers under 17 years old are not buckled up or properly restrained. A safety belt violation can result in a fine of $100 to $200 or mandatory attendance at a traffic safety education class dealing with child safety seats and safety belts.
Unrestrained drivers and passengers 15 years old and over who are not wearing safety belts in the front seat can be ticketed directly. Fines range from $25 to $50 normally according to the information we have read.
So, yes if you are 16 you can receive a ticket in Texas for not wearing your seat belt. You can read more about the Texas Occupant Restraint Laws on the TX Department of Public Safety (DPS) site.