To answer your question....
No, Austin, it is NOT illegal, as a matter of state law, to carry pepper spray here in Texas. [I'm not an attorney, just a cop with a decent grasp of the Penal Code.]
It's similarly not against state law to carry a Taser.
But if you wield these items against another person without a solid self-defense purpose, you may be charged with Assault, Assualt Causing Bodily Injury, Aggravated Assault, or, in the instance of the victim's death, Manslaughter or Murder. If you simply spray pepper spray in a public area, you may be charged with Disorderly Conduct.
Be aware, however, that local ordinances and regulations may differ from the law, and you have to use the stricter standard.