"Because the car drives just as it always has, just after about 3 miles it overheat."
I don't mean to sound condescending, but that's because the car has heated up in those 3 miles. At the very least you have either not "burped" the system getting the air out, or the thermostat might be stuck closed. There is the greater possibility when you ran your car low on oil you damaged the bearings, cylinder walls and pistons (amongst other parts). That has creates significant internal friction when the engine is running. It becomes more intense as the engine heats up. So, yes, while you may have a blown head gasket or a cracked head you may also have greater damage than that. If you come away with only a blown head gasket consider yourself fortunate. But, given what you stated I'm inclined to think that there can be more significant damage.
The first place I'd start is removing the spark plugs and observe them for water/coolant. Then I'd run a compression test. Drain the oil into a clean container and look for the milky carmel color of water in the oil. Then slowly pour the oil off into another container and see what is in the bottom (sort of like one pans for gold). If there are metal particles both silver-ish and copper colored then the bearings are probably shot.
Simply put the fluids in an engine are fundamental to it operating as designed. The absence of them is like expecting a human body to function without water and blood. I've made the mistake of thinking I could get home with a blown radiator on a cold, rainy day. And, I paid the price for that kind of thinking too.