That is, in fact, ozone. You're not alone. I often smell it ahead of big storms as well. Of course, I also smelled it after watching the maple tree in my front yard get zapped 20 feet away with nothing but a window screen and air between my face and $DEITY knows how many kilovolts.
There is some variation in how sensitive people are to individual odors. Picking up the ozone smell before storms seems to be sufficiently rare that a lot of people end up wondering if they're the only one.
Anyway, as I said, the ozone is produced by the electrical activity in the storm--if you're curious, you can get a smell of ozone off of artificial sources of high-voltage electricity as well. Hanging around a Tesla Coil or Van de Graff Generator ought to do the trick.
And hey, look at it this way, it's not the storm itself you're noticing--you're actually smelling lightning. How cool is that?
I've always been able to smell this before a storm as well. I remember when I was a kid and I would tell my parents, friends, whoever, this fact and they would just think I was crazy because no one else could smell it.
I have very poor eyesight, so my hearing and sense of smell are extremely acute.
