37.125 refers to causing alarm. If it is noticed and reported then it is assumed to have alarmed someone.
A better section for your answers would be Penal Code 46.03 (a)(1) and penal code 46.03 1(f) and discusses carrying. Places weapons prohibited.
(a) (1) is physical premises of a school. That means ALL the property.
(f) specifically does not exempt CHL from offense.
Storing handgun in your car on a campus has been ruled (by TX Attn. general ) to be OK if you have a CHL. Walking around in the parking lot carrying concealed with a CHL is not OK.
Every time the laws change (every two years) I go to a Legislative Law update session. They are for peace officers to be informed about any new laws or about any new Attn. General Opinions which are called "case law". I'm a university police officer. On a campus, two sets of laws apply...Texas Penal Code and Texas Education Code.
Strive to live up to the opinion that your dog has of you.