Depends on how long it ran after overheating ... If it just blew steam out, it probably didn't damage the engine. If it ran for 5-10 minutes after that ... do a compression check.

Did you recently change the coolant? That's when they usually overheat, after being filled back up due to air being in the system.

The thermostat might also have stuck. You can test it in a pan of boiling water on the stove. Use a kitchen thermometer and make sure the thermostat opens at the rated temp.

To check the radiator itself, (let cool down)remove bottom hose and cover bottom outlet with your hand. Fill radiator with water from a garden hose. When full, remove your hand. The water should pour out in a huge rush the diameter of the bottom outlet. If a smaller stream comes out, the radiator is blocked internally.

I hope nothing is seriously damaged. Do you live in a hot state? What temp was it outside?