A fun look at the meaning of "peinlich", how to say that you're embarrassed in German and some more words like shame or disgrace :).
peinlich, die Pein, der Schmerz, das Schmerzmittel, die Schande, bloßstellen, sich blamieren
The original idea of this root was:
paying, atoning, compensating
And the family has focused on the more “severe” side of this, as we can see in the English offspring pain and penalty.