Welcome to the forum.
The Motorist Protection Act says is what you are looking for. Search on it on this site (also "MPA" and/or "traveling" and similar terms) and you will get quite a few threads on it.
You can find texas statutes here:
http://www.statutes.legis.state.tx.us/" onclick="window.open(this.href);return false;
although they are not completely updated with the results of the last session yet. I don't believe anything affects the relevant part of the Penal Code, which reads as follows:
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.
(a-1) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun in a motor vehicle that is owned by the person or under the person's control at any time in which:
(1) the handgun is in plain view; or
(2) the person is:
(A) engaged in criminal activity, other than a Class C misdemeanor that is a violation of a law or ordinance regulating traffic;
(B) prohibited by law from possessing a firearm; or
(C) a member of a criminal street gang, as defined by Section 71.01.
The law is written to describe what is a crime, not what is not a crime, so if you are not doing anything described above, then you are good to go. i.e. your gun is
not in plain view, your
not engaging in criminal activity other than a traffic violation, you are
not prohibited from possessing a gun, and you are
not a gang member, then you are legal to have a loaded gun in your car.
Technically under federal law you still may not have a loaded gun in your car if you are within 1000' of a school, but as a practical matter this is only enforced when you bring attention to yourself with other illegal or unusual activity.
However, I am not a lawyer and you would do well to read all the laws concerning firearms for yourself, as I will not be around if you get crossways with the law.