The cotton gin is what made a large-scale cotton industry viable at all. Picking seeds out by hand is so labor-intensive that cotton clothing was an absurdly expensive luxury before that.
But really, the growth of the South during the first half of the 19th century was largely due to immigration patterns. The plantation owner class was largely already-wealthy men from the British merchant class. Due to British class structure, they could never equal even the poorest, lowliest members of the aristocracy, despite their obvious superiority. Moving to America gave them a chance to treat business acumen and wealth itself as an elite class. Next down the list were the scots-irish indentured servants, mostly rebels and criminals and their families. England could either hang them, or sell them to the plantation owners to work off their fines and immigration costs. They provided supervision over the slaves. The slaves were brought over to meet growing labor demand. So it wasn't so much new tech as the colonization and working of large tracts of previously wild land. (Remember, slaves were brought from Africa around the same time to work the sugar plantations of the Caribbean as well - the economics were compelling)
