Don't use one of those adapters that converts a 3 prong to a 2 prong unless you know for certain that the socket has been properly grounded.
You can install a new breaker in the service panel and run 3 wire Romax to your grow. Then you can install a 3 prong outlet (preferably a GFCI). Buy a basic wiring book and follow the instructions exactly. Electricians don't charge much compared to morticians, so don't be afraid to hire a pro.
Add a 20 amp, not a 15 amp. The cost is the same and the 20 amp is no more hassle than the 15 amp. While you're at it, consider installing 2 runs of wire so if your grow ever needs another breaker, the wire will already be in place.