I agree with Athlyn Green--Alexandrite is the "official" (do they change them every year or what?) birthstone of June, and being a June baby I have a number of pieces of Alexandrite jewelry--all made with lab-created Alexandrite because it is very difficult to obtain naturally occurring Alexandrite (most of the world's known supply is in Russia, according to some research I did about 4 years ago--I have some friends who escaped from Russia with their children), and it so happens that exporting Alexandrite was a crime because Alexandrite is considered a national treasure, they said.
There are basically two modes of thought about created stones: (1) is that they cheapen the real thing and are beyond worthless, (2) is that they are completely pure and the color-change amount can be tweaked somewhat by putting the stones in an oven until they're the proper color and make appropriate color changes (a risky procedure that sometimes results in a useless gem). Personally, I like #2 because I know nobody risked their lives bringing it out of Russia. And, I like the flawlessness.
So, on the surface, it looks like whatever you paid for it at the garage sale was probably a HUGE bargain if this is indeed alexandrite (especially natural alex.) in a white-gold setting. I'd suggest taking it to your local jeweler and see if she can make a final ruling on this and make sure the gem(s) are properly set and not in danger of falling out. A thorough cleaning is also a good idea that can be done at the same time by the jeweler in an ultrasonic cleaner (they should offer to do this cleaning for free). You may want to get insurance coverage on this piece if you don't already have an umbrella policy that covers it (minimal charge) or ebay the item if you'd like the money. Hope this helps! (P.S. I tried to take photos of a few of my alexandrite pieces, but they all came out fuzzy. Hey, I'm a writer not a photographer (generally speaking).)