In 1860, the US exported:
$192 million in cotton
$46 million in manufactured goods
$22 million in grain
$17 million in meat and dairy products
$16 million in tobacco
Total exports were $316 million.
Total
US GDP in 1860 was about $4.4 billion.
Total exports were about 7% of that GDP
Total cotton and tobacco exports were were about 5% of that GDP.
I think the problem is that, rather likely Smoot and Hawley, you do not really grasp the importance of seemingly small external inputs in an economy. When in the 1930s the US manage to own goal about 60% of their export markets amounting to a mere 3.6% of GDP their domestic economy was basically bimated, that is diminished by half.
However the good news for the US is that most of the pump priming effect that drove the North was created in the North. The main form cotton exports took for example was as raw cotton, thus the only direct input to the economy of the Northern states was the shipping fees charged by Boston and New York etc based ship owners. Now it has been pointed out that raw cotton that might previously have been considered an internal commodity has now become an import but so too has manufactured goods such as clothing being sold back to the Southern States become an export. It is likely that clothes produced in workshops in Boston and New York are going to remain competitive in the Confederacy compared to those produced in Birmingham (the English one) and London in Confederate markets thanks to the shipping differential. It would likely be awhile, even assuming the Southern elites break the habits of a lifetime, before Southern investment produces large scale internal suppliers of manufactured goods.
Rather like the loss of the 13 Colonies the US has lost a war but gained an export market. The difference here, that rather complicates matters is that rather than reducing defence costs as happened to the British post 1783 is that it might rather drive up the costs as border fortifications and standing armies might be need to be maintained.
Now of course it is hard to see a clear picture without knowing how exactly the rebels won and what they made off with but a few things may or may not follow the OTL trajectory.
The US merchant fleet for example was crucified post war by the refusal to allow owners to return their ships to the flag and continuing protectionist policies on shipping rights. However in this scenario a lot of ports domestic are now effectively foreign or at least outside US control making the provisions forbidding foreign ships carrying goods from a northern port to one of them a bit nonsensical. A more open policy on shipping and especially a more open policy on where US owners can source their ships could well see the US continue to posses an effective merchant fleet into the late 19th Century. Not a given mind but on of the possibilities opened up.
The main drag on the Northern economy and indeed the Southern one but we are not looking at them here, relative to OTL is likely to be additional Government spending and thus borrowing and taxation on armies and fortifications and quite possibly the Navy. The rump US may well be more heavily armed than the entire OTL US but this will come at a long term economic cost as it transfers money from more productive and self-sustaining pursuits.
The biggest difference of course would be the Inner American Border. This IAB would need policing for tax purposes as it is highly likely to see a lot of traffic and I would greatly doubt either the USA or CSA would wish to give up those juicy tariffs nor would smugglers wish to pay them. In fact from a literary point of view the IAB could really be quite exciting with dashing villains and evil customs men or vice versa depending on an author's biases.