I'm no expert at these, but I would assume it's not very common for these to be counterfeit, especially if they've been in your family since the civil war.
Well, the provenance of a note cannot usually be confirmed beyond living memory, unless a family has been more meticulous than usual about its oral history. And Confederate notes are very widely copied, and have been ever since the War itself. It is, of course, not a crime to counterfeit Confederate currency, as American law never recognized the Confederacy as a legitimate government. It is only a crime to fraudulently sell a fake as genuine for an inflated price.
Lists of serial numbers of frequently-copied Confederate notes are maintained all over the Internet; I use the oldest one, Crutchfield's Currency
By that list, the OP's notes are both OK.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis