Does an oath take effect when one denies taking an oath, and is expiation obligatory for an oath in which one's assumption proves to be untrue?

The reason for what the sister is experiencing is her succumbing to whispers (waswas) and not ignoring them. These whispers are from Satan to discourage her from worship. Her statement, "I swear by Allah the Almighty, I did not say I would fast on Thursday," has no consequences, and similarly, her swearing an oath about something she believed to be true, but which later turned out to be false, also has no consequences.