The work 'sick' does come to us from the Germanic root. In fact, the Dutch name for a hospital is 'Ziekenhuis', a house for the sick, as it were.
As for the usage of the word 'sick' in a positive sense I would imagine that it's a 'street thing' and incorporates the same playful irony as when some people use the word 'bad' as meaning good. It's more to do with slang than Schleswig-Holstein methinks.