Personally I choose to believe she is a vampire, just an extremely janky-ass one. That’s a really funny concept in itself, but also the alternative is a bit too depressing, for me.
If she isn’t a vampire, I don’t really think it’s something came up with by herself. She kept talking about her noble lineage and even mentioned having relatives that explicitly told her to not get close to people. So, from my read, it would be less just a weird lady who’s deluding herself (which would be kinda funny), and more someone that was deluded (and essentially had her life ruined?) by her family. Which would be a bummer.
So I choose the funnier interpretation. The idea of her being a powerless vampire also reminds me of some of the student council stuff in Kitakubu, or even the magical girls from Lollipop. “Special thing, but so limited and janky it’s almost indistinguishable from a normal person” just feels like a thing the author would do.