The important thing is why did it get hot? Were you using it for a resistance heater or other high wattage device? The breaker should have tripped if it was overloaded. You should probably let the landlord know by email or written notice.
I'll send myself a letter, then.
It's a smell I know well. The usual cause is either a wire in the socket or plug that is not properly tightened, or a pin on the plug that is too small in diameter for the connectors in the socket, so it is loose. These cause heat build-up. The heat further deteriorates the bad connection, making it even worse (hotter)
A good rule of thumb is to unplug after use and hold the plug near your cheek to test if it is radiating heat.
Also, of course, never load a single socket with a stack of multi-socket adaptors, thus exceeding the wall outlet's rating.
Have been around electricity for a pretty long while....recognize the smell you're talking about, just have never associated with fish. Generally an indicator that you need a 20 amp receptacle.....electric portable heaters are usual culprits