As I understand it, cotton and tobacco were the USA’s biggest exports before the Civil War, but somehow the North made more money off them than the South did.
Absolutely true. Thanks to the laws created by Northern control of Washington DC, much of the money the South produced ended up in New York and Washington DC. (Same corrupt bastards still running the nation today.)
The South produced 72% of the total trade value with Europe.
Here is a visualization that demonstrates where all the money ended up.

They deserved it
They were better than us morally
Just ask them
Course most northern freepers who delight in equating southern ancestry with nazis didn’t even have folks here in the fight unlike native southerners who have a fairly undiluted ancestry stream from 1600s on
These south bashers ancestry were too busy with taters or cobbling in Eastern Europe or north of the Baltic absorbing and fomenting collectivist messianic ideologies to bring over here with them to infect us in the way wokism does now
Fabians
Not the crooner
Cotton was almost entirely a product of the Deep South, in 1860 its exports totalled about $200 million, or about half of the Deep South's GDP.
Tobacco was a product of mostly Union states, including Kentucky.
In 1860 its exports totalled about $24 million, or roughly 10% of Border states GDP.
As to who, exactly, "made money" off those crops, obviously, everyone who handled or processed them got paid something, as did, for example, the carpenters who built the large estate homes of wealthy Southern planters, and Northerners who manufactured the iron stoves or carpets that went in those mansions.
So, how much money was left over for luxury imports after all the bills were paid, and new slaves "purchased" to expand his operations?
Typically, not very much, if any, and so naturally, we'd expect the great slav-ocrats to seek relief from their obligations by declaring secesdion & war on their creditors.
A clever move, right? Or too clever by half?
“As I understand it, cotton and tobacco were the USA’s biggest exports before the Civil War, but somehow the North made more money off them than the South did.”
ANYTHING from agriculture, from any part of the country, north or south, provided less profits (more competition among farmer sellers) than to large traders, distributors and exporters. It was not a north-south thing as much as an industry and trade over agriculture.