My 2005 Cobalt started running at 230 degrees and when I checked the coolant level there was none in the resevoir? Should I be worried about the engine being damage? I drove it for about 10 minutes without it steaming, etc..

Your coolant has either gone to the outside of the engine via broken hose, radiator leak, heater core leak, or head gaskt to outside. OR it leaked into your engine via head gasket leak to one or more of your cylinders. If this is the case, then you might notice water issuing from your tail pie (after you put water back in it of course)

You probably didn't sustain any major damage. You should be concerned about the loss of coolant. If there is no evidence of a leak where you park then it;s possible you could have a leak that only happens with the engine running. Being a late model GM car, it uses a coolant called DexCool. It is pink in color and is known to cause deterioration of certain gasket materials. In particular, the upper intake plenum gasket. These leaks are difficult to find. With the engine running, use a bright flashlight and look for coolant puddling around the edges of the intake plenum. Also check your radiator and heater hoses for pinhole leaks that could open up when the coolant gets hot. Be sure and keep a close eye on your coolant level until you find out if you have a leak.