Engine heating and replacing spare part

Hello, this is my problem. So my coolant leaks and I maintain to fill it regularly. But one day I forgot the the coolant cover open and drove for about two hours without speeding. No heating problems. Next day I saw the coolant. I have fill it again and closed it. Car start heating. Apparently it still has air inside the coolant even tho I have filled it with water. The start to over heat so fast. I have stopped and waited for it to cool. And drove home. ( Not far from where it heated 250 meters). Any way I have taken out all of the air in the coolant refilled it and drove again. And this time no heat what so ever. Everything is fine. Then I hear clicking noise either in the engine or the fan. The car stops I managed to get working again but every time I push the gas pedal the noise become even louder and the car stop again and by stop I mean the engine is dead. I called a tow truck took it to a mechanic.

here is the important part.

the mechanic says nothing major is damaged all you need is to change the radiator and the thermostat tube the front one.

is that correct? By correct I mean seems reasonable?
and do I need to change also the back thermostat tube?

Thank you all.