No, these are three different meanings.
"Herself" in A emphasizes that it's she who cannot sit up, probably in contrast to someone else you're talking about who can sit up.
"By herself" in B indicates that she can't sit up without help. It implies that she can sit up with help, but not without.
"For herself" in C refers to the purpose of sitting up, i.e. it's saying that she couldn't sit up for her own sake, or something like that. This is a strange sentence that I wouldn't expect to hear.