Say I am going from South Carolina in 1810 to Pennsylvannia. A PA dollar would be worth more/less than my South Carolina dollar, and likely no one would have use for my South Carolina money. Would I have to travel with a bunch of gold to make purchases on the trip?
I hope this isn't too vague. It just seems tthat everything would be inconvenienced by the monetary system...
In 1810 you'd be using US Dollars.
The differing currencies of the States under the Articles of Confederation was one of the primary reasons for scrapping it and switching to the Constitution.
During the AoC period you'd likely use Spanish reals, British pounds, or whatever the French currency was (I don't think it was francs until after the Constitution was passed).
You either had to travel with a bunch of gold or do the following - stop along your route several times to exchange South Carolina currency for new money in North Carolina, Virginia, and Maryland. It would have been really inconvenient. Let's say you go too far on your journey and no bank would take SC currency, or let's say you choose to carry all that heavy gold instead and get robbed? '
You can start to see why creating a nationalized currency proved to be a big deal in terms of both improving our economy, but also making business more national or at least regional.
The National Banking Acts in 163 and 1864 further solidified the transition into a national currency and banking system.