See #1597 and subtract normal expenses from total expenses. That gives you a fairly accurate figure.
Southern infrastructure spending was largely privately financed. That included railroads, dredging, and roads.
You can be 100% certain that whatever federal largess was being handed out in those days, Southern politicians received no less than their "fair share".
But in fact most "infrastructure" work then was privately or state-governments financed.
Federal debts in the late 1850s were near all-time low levels.