I have a 1998 3.8 camaro. Every time I turn the A/C on, the passenger side gets filled with water, is there something I can do to fix it myself, or do I have to take it in to the shop??

 

Its your heater core.

 

The heater core would be leaking at all times, not just when you turn the AC on.
There is a catch tray under the dash below the AC evaporator coils. The tray is connected to a hose that carries the water condensate out and dumps it under the car. Make sure the catch tray is in place ,and the hoseis not cloggedand in one piece.