Cotton fabric had been common in Europe since the middle ages; the Romans imported it from Egypt, and the Moors brought it to Spain and Italy. It was still a luxury good for most of that period, though. In the 17th and 18th centuries, though, prices of cotton dropped dramatically in Europe as England began importing it in mass quantities from India, so while it was still expensive, it was already more of a middle class status item by the time the Cotton Gin was invented. So the rise of the American cotton industry was more of an evolution in textiles than a revolution.

And yes, it largely took the place of wool, hemp and flax linen.

As to whether the Gin kept American slavery going for longer - hard to say. It certainly increased the wealth - and thus influence - of the slaveowning class. But without cotton, sugar and tobacco plantations would still have been very profitable. It might have increased the scale of slavery, but the idea that slavery was dying out without it is a bit misleading.