Did you mean I could damage my engine so quick? Because I was driving a little but temperature on some point was coming to the normal level.
How can I say if engine been damaged?

If it really overheated damage can be done--even if only once. If the temperature just got a little higher than normal, I wouldn't worry about it.

Coolant/oil leaking into the combustion chamber, loss of compression, damaged valves, blown head gasket are the normal signs. It may take a while for the damage to appear.