Here is the applicable law.
PC §46.03. PLACES WEAPONS PROHIBITED. (a) A person commits
an offense if the person intentionally, knowingly, or recklessly possesses
or goes with a firearm, illegal knife, club, or prohibited weapon
listed in Section 4S.05(a):
(1) on the physical premises of a school or educational institution,
any grounds or building on which an activity sponsored by a school or
educational institution is being conducted, or a passenger transportation
vehicle of a school or educational institution, whether the school or
educational institution is public or private, unless pursuant to written
regulations or written authorization of the institution;
The offense is classified as a Third-Degree Felony and is punishable by 2-10 years in prison and up to $10,000 fine.
Premises is defined as a "building or portion thereof."
PC46.035(3) "Premises" means a building or a portion of a building. The
term does not include any public or private driveway, street, sidewalk
or walkway, parking lot, parking garage, or other parking area.
This is directly from the Texas Penal Code. Do note that having something in your car in the parking lot could be grounds for expulsion under circumstances that would virtually ensure that you would not be admitted anywhere else, except some on-line school that has about zero credibility in the job market.
I am not an attorney. I just know where to find the law on the DPS website.
See a lawyer if you still can't make up your mind.