Let me find the statute...
Walking from your apartment to your car meets the requirements above.Sec. 46.02. UNLAWFUL CARRYING WEAPONS. (a) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun, illegal knife, or club if the person is not:
(1) on the person's own premises or premises under the person's control; or
(2) inside of or directly en route to a motor vehicle that is owned by the person or under the person's control.
However, it seems that walking FROM your car, to your house is not.