Radiator burst and I kept driving the car, how can I check to see if it caused any engine damage?

Hello,

What you tried to add coolant into the radiator to see where it is leaking from?

Typically, one of the two radiator hoses and burst or simply come off due to being worn.
Visually do an inspection to see if you can tell where the leak might be coming from.

https://www.2carpros.com/articles/how-to-replace-a-car-radiator
https://www.2carpros.com/articles/replace-radiator-hoses

As for if the engine is good or bad, you will have to first see if you can have coolant in the system, if the coolant stays in the radiator, then try to start it if it starts runs fine without overheating it should be okay.

But the first step would be to figure out where the leak is. Then see if the radiator holds coolant. Keep in mind that sometimes a bad radiator cap and let coolant come out of the radiator.

You can also do a pressure test to see if the radiator is leaking.
Here is a helpful video:

https://youtu.be/W8kra65m15c

Please let me know what you are experiencing.
Thak you.

The radiator is leaking and cannot hold even one oz coolant. It is evident for me it burst when I was driving, since I didn't notice any overheating for twenty miles driving. So before starting the car, I need to replace the radiator. I need to check if the engine is fine or not, otherwise the money I will spend for the radiator would be a lost money.

Without starting the engine, there is not effective way to tell if there is internal damage (unless the engine gets taken apart).
Did you see any smoke coming out of the tailpipe when it over heated?
If the head gasket was blown it typically emits white smoke.

https://www.2carpros.com/articles/white-smoke-or-steam-coming-from-the-exhaust-pipe

Check the oil, if the head gasket were blown due to overheating you could get coolant in the oil. Which will make it a milky color.

I saw white smoke coming out of the engine top but for oil I need to check it tomorrow, although I only drove with the highest temperature for five miles. Therefore, I am still not sure if the coolant could leak to oil during this short time.

Before this incident, I saw the coolant bubbling so the gasket was building pressure to the radiator.

If the head gasket were to blow you will get white smoke out of the tailpipe. As the white smoke from under the hood is likely just steam.

Depending on few variables 5 minutes might not do permanent damage to the engine.

Let me know what you find on the oil.

I checked and seems actually the hose back of the engine between thermostat and the engine burst.
Why the engine builds pressure in the radiator?

Thanks.

Well, that is good, that it is just a hose. Much easier to replace.

If you are asking about coolant system pressure, keep in mind that the coolant system only become under pressure when it is heated. As you know heat creates pressure by expanding / energizing the molecules of the coolant and other component.

Let me know how it turns out or if you have any questions.

I have noticed before the coolant is bubbling. So, what could be the reason for the bubbling? Can bubbling add pressure to the radiator? If it is due to the faulty head gasket, is there an easy way to fix it?
Thanks.

Bubbling indicated rising pressure in the cooling system. It could be due to air in the cooling system. Which will significantly increase pressure as air expands at a faster rate. Most common cause for air in the cooling system is a leaky/blown head gasket.
Unfortunately, if the head gasket is blown there is not really an easy way to fix it.
There are chemicals that can be used which may or may not help.
Check out this video that we did on those chemicals to have a better understanding:

https://youtu.be/Xi41RFMP8Ow