The main problem is that, while factory-loaded .38 S&W ammunition is still made and is available, it is difficult to find and expensive. You will not find it at the local Wal-Mart, nor in most gun shops, as it is a low-demand item. That is why most people who like to shoot the old top break revolvers (and some newer ones) chambered in .38 S&W load their own.

Yours is legally an antique (pre-1899) and is not regulated as a firearm in most jurisdictions.