Engine overheating

My car reads, "engine overheated. Turn engine off!" I read the manual and stopped to look at my car. Apparently, I had no anti-freeze in the car. I bought some 50/50 and put it in the DEX-COOL container to the fill line. The lights went off and I made it the 3 miles home at which point it came on again. I let it sit in the drive for several hours when I tried to run it back out to the intersection, 3 miles away. The same warning reading came on, so I stopped the car. The antifreeze level hasn't gone down from what I can see, so I am guessing it isn't getting to the radiator. Would this just be a case where I need to get the radiator flushed, or would it be a water pump gone bad? The car has almost 72,000 miles on it. Worst case scenario what could this be and what will it potentially cost me?