First of all, if you put the antifreeze into the overflow reservoir, and did not check the level in the radiator; it is highly likely that the coolant level in the radiator is still very low. This would make the engine overheat very quickly. There is no automatic connection between the reservoir and the radiator. Fluid only moves between those containers when there is a siphon established between them. But whenever the coolant level becomes very low, the siphon will be interrupted. That is why you have to check and refill the fluid in both containers separately.
Secondly, adding a significant quantity of pure, undiluted coolant to an engine will make it more likely to overheat. Antifreeze is designed to be mixed with about 50% distilled water. If no water is added, the coolant will not be able to transfer heat from the engine adequately. And that will lead to overheating. But some types of coolant are sold pre-mixed with water. That type can be used without adding water.
The original cause of the overheating may have simply been that the coolant level in the radiator was never checked. But it also may be that the electric radiator fan is not working (usually because of a failed thermal fan switch), or the thermostat is stuck shut, or the radiator, water pump or a hose is leaking. The sure way to locate any leaks is to have the system pressure tested, by attaching a pressure pump to the radiator, and pumping it up to the normal operating pressure. Any leaks will quickly become apparent.
Sometimes when an engine overheats, the head gasket will be damaged and begin leaking coolant into the engine's cylinders or the crankcase. A cylinder head can sometimes become warped or cracked during this process. And that can be a major expense to repair. If a pressure check indicates that coolant is leaking into the engine; the cylinder heads will have to be removed, inspected, and either remachined or repaired. New head gaskets will have to be installed whenever the heads are taken off. If this kind of damage is suspected; it sometimes is more practical to replace the car, rather than pay for the repairs.
I hope this helps!!!