"After" may work logically, but that is not how people actually talk. They say "in a week."
That's possible, but more likely you would hear "in nine days."
I think (perhaps I'd better say "thought") that "in 9 days" means: tomorrow or the day after tomorrow or on the third day or on the 8'th day or on the 9'th day.
And I think that "after 9 days" means: not tomorrow or the day after tomorrow or ... or on the 9'th day, but on the 10'th day.
Am I wrong SoothingDave?
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