Even though I haven't received my own CHL yet, I would never show or pull my weapon unless I was in immediate need of using it against a dangerous or harmful threat. There have been too many instances of GGs getting in trouble for doing so, some of which had their CHLs revoked for their action. So, until we get an open carry law passed I would keep it concealed until I was drawing it to use against such a threat.
Not knowing your location, or the particular VA hospital you were visiting, I would also consider jbirds' suggestion of moving your car to a different area in the parking lot. If it's the VA hospital in Dallas, then that would have been a good option no doubt. Don't forget that driving your car very slowly can also be very effective in getting someone on foot that's very persistent out of the way (unless they lay down in front of it), but then again even that can become a fine line between getting away from that person and assault with a deadly weapon if you're not careful.
Also, even though your cell phone wasn't working at the time, if you go through the motions like you're actually having a conversation with the police, you may have been able to fake the other person out enough to make them leave the area if they suspect (overheard) that the police were already in the area and would be there in less than a minute. Start describing the character in detail and they'll usually tuck tail and leave quickly.
With regards to leaving your pistol in the car after having a nut case see you with it, there's always that possibility of theft. If you don't have a car safe, or at least a trunk that can't be easily opened from inside the car (push button or lever is locked, or located inside a locked glove box), I would have been uneasy until I got back out to my car, too. However, judging by the portrayal of the character that you exposed your weapon to, he probably wouldn't even know that you didn't carry it in with you (believe me, unless you study for the CHL or are involved with the laws due to your profession or some other reason, most people have no idea of the restrictions or permissions involved for CHL holders).
Overall, I'm very glad that you were safe and the jerkette finally left you alone!
