"On January 7, 1886, the Philadelphia schooner Crissie Wright, on her way from Baltimore to Savannah, was forced to beach herself three miles east of Beaufort [North Carolina] during the bitter winter of 1886. Six of the crew drowned and froze to death. Two of the crew were lost at sea and three were buried in a common grave in Beaufort's Old Burying Ground."
—found here (click for more details).

I haven't found a description of the cargo, but I doubt that rum-running had anything to do with it.

Also, I haven't found any song about the event.

Some sources spell the name "Chrissie Wright."

(Refreshing a 12-year-old thread here.)