What races are available for play?

Are only the core races available, or would I be able to play a Half-Celestial Human, an Aasimar, or a Drow?

Only the races of the PRPG; i.e. dwarf, elf, gnome, half-elf, halfling, half-orc and human.

This is in the Guide to Organized Play on Page 13 under "Race and Class"

After you finalize your PC’s ability scores, you must choose your character’s race and class. All of the options in the Pathfinder RPG Core Rulebook are available to you with some minor adjustments.

The specific races you've mentioned are not indicated in Chapter 13 (Additional Resources).

If you haven't already downloaded the Guide to Organized Play, you might want to do so here.