Finish dripping down on the main level ceilings?

Q: My upper level floor is my main level ceiling (craftsman style home). I did it wrong, and I have already finished the ceilings of the main floor. How can I finish the upper level floor without the finish dripping down on the main level ceilings?

Can I completely seal the upper floor in any way, so that any spills from above will not drip to below?

A: Is this tongue and groove? If there are no large gaps between boards, I don’t see why the finish on one side of the board would cause a problem with the other side.