You are correct. You drilled right through the passenger airbag module. You are incredibly lucky it didn't deploy while you were drilling or immediately upon turning on the key.
You've got some work and some expense ahead of you, but here's a site that will explain everything you need to know about airbag systems, airbag lights and resetting the system. It shows you the location of the components and the procedure for diagnosing and resetting airbag lights.
http://www.airbagsolutions.com/
You can check to see if your car is listed here.
http://www.airbagsolutions.com/vehicles_list.aspx
If the light is flashing on your car it's telling you there's a problem. On some vehicles, the light is flashing a two digit code. Once you know the code, you can most likely repair it yourself. There are fairly easy procedures that most people are capable of repairing.
Airbagsolutions.com has the fault code charts to tell you what is wrong and how to fix it!
Some vehicle manufacturers let you access and reset systems without a scanner (like Toyota, Lexus, Nissan, Infinity, Honda, Acura, Ford, Lincoln, Mazda & Mercury) and some require a scan tool.
Although it’s a pay site ($14.95/day), it’s a lot cheaper than going to the dealer