Texas law brackets by age groups. For details follow this link to Texas Child Labor Law
As best as I can tell these are the only restrictions:
IF YOU ARE WORKING FOR A PARENT OR GUARDIAN THEN:
This chapter [ section of state statutes ] does not apply to employment of a child:
in a non-hazardous occupation;
under the direct supervision of the child's parent or an adult having custody of the child; and
in a business or enterprise owned or operated by the parent or custodian.
IF YOU ARE BETWEEN 16 AND 17 YEARS OLD THEN THESE RESTRICTIONS APPLY:
Prohibited Occupations for 16- and 17-Year Olds
These occupations are commonly referred to as "Hazardous Occupation Orders" and include work:
1. In or about plants or establishments manufacturing or storing explosives
2. Involving the driving of motor vehicles and outside helpers
on any public road or highway
in or about any place where logging or sawmill operations are in progress, or
(Under certain conditions, driving a motor vehicle for a commercial purpose is NOT considered a hazardous occupation under state or federal law.)
3. Connected with coal mining
4. Involving logging operations and sawmill operations; and forest fire fighting and forest fire prevention operations, and timber tract and forestry service occupations
*5. Operating or assisting to operate power-driven woodworking machines
6. Involving exposure to radioactive substances and to ionizing radiations
7. Operating or assisting to operate power-driven hoisting apparatus such as elevators, cranes, derricks, hoists, and high-lift trucks
*8. Operating or assisting to operate power-driven metal forming, punching, and shearing machines
9. In connection with mining, other than coal
*10. Operating or assisting to operate power-driven meat processing machines and in slaughtering, meat and poultry packing, processing, or rendering.
11. Operating or assisting to operate power-driven bakery machines
*12. Involving the operating of power-driven paper-products machines, balers and compactors
(Under certain conditions, loading a baler or box compactor is NOT considered a hazardous occupation under state or federal law.)
13. Manufacturing brick, tile and kindred products
*14. Operating or assisting to operate power-driven circular saws, band saws and guillotine shears, abrasive cutting discs, reciprocating saws, chain saws, and wood chippers.
15. Wrecking, demolition and ship-breaking operations
*16. Roofing operations and work on or about a roof
*17. Connected with excavation operations
The hazardous occupation orders denoted with an asterisk (*) have apprentice or student-learner exemptions.
Apprentice and Student Learner Exemptions
employed in a recognized apprenticeable trade;
work is incidental to training;
intermittent, short, and under close journeyman supervision; and registered or under written agreement about work standards.
enrolled in authorized cooperative vocational training program; and employed under a written agreement providing that:
(1) work is incidental to training;
(2) work is intermittent, short, and under close supervision;
(3) safety instructions are given by school and employer; and a schedule of organized and progressive work is prepared.