The deadline
Tex. Civ. Prac. & Rem. Code § 16.003(a)
Two years from the day the cause of action accrues, which for most injuries is the day it happened. That is the deadline to file suit in court, not the deadline to notify an insurer or to start a claim. File late and the case is dismissed regardless of how clear the liability was.
Three situations change that date and they are the ones worth checking rather than assuming. A wrongful death claim runs two years from the date of death, which is a different date from the injury when someone survives for a period. For a person injured as a minor, the period is generally tolled during minority, so it typically begins at eighteen. And a claim against a governmental unit is the trap: the Texas Tort Claims Act requires formal written notice, and many cities set that period by charter at six months or less, which can bar a claim long before the two years are up.
The practical deadline is much earlier than the legal one in every case. Surveillance video overwrites in days. Commercial truck data is retained for months. Vehicles get repaired or sold. The date that actually decides most claims is the one by which the evidence still exists.