Yes, you can legally carry a loaded coach gun in your vehicle here in the great State of Texas. Excellent choice for self-defense. Buy some of the federal tactical 8-pellet buck shot and you can decimate someone out to 50 yards.
Seems to me, if you have time to unstow and get a shotgun into position to fire, you could've just driven away.
Stuck in gridlock traffic? Car disabled? To the OP, just carry a pistol, perfectly legal as long as you can legally own it, it is concealed, you aren't a gang member or committing a crime.