It does sound like your alternator did, in fact, die. Once they go, you're not going to get very far as the battery will soon become undercharged, and start lighting up your dash like a Christmas tree. The car will stop eventually.
It's easy for your shop to test the alternator. Mine was going from working to not working, working to not working....maybe that's the reason I made it to my shop, and wasn't parked in a lot like you were. If yours just plain old died, that could easily strand you.
The good news is that it's an easy fix. I had a shop do mine, as I was taking my GF away for the weekend the next day, but figure I could have done it myself. My shop charged me about $650 for everything, which included a new belt and the replacement of one of the pulleys that looked a touch iffy. The belt and pulley added about $70 to the cost.
Good luck. It should be a pretty simple deal.