Here are my suggestions:
'smug' - showing very clearly how pleased you are about your own achievement.
It describes how someone appears or looks.
Two people are running in a race. At the end of the race, one of the runners says
"He looks so smug! But he only just beat me to the finishing line. It was very close."
'conceited' - being excessively proud of themselves or their ability.
It describes how someone is or behaves.
He was so conceited that he could not possibly imagine losing a race.
I hope these definitions and examples are helpful to you. Happy studying!