Is the questioner's action correct in ignoring the many consecutive doubts—which afflicted her in her prayers and acts of worship—and not repeating the prayers, assuming they are whisperings (waswas), despite her forgetting the number of times she doubted?

This doubt is a clear case of waswas (whispers from Satan), and its cure is to distract yourself from it and pay no attention to it whatsoever, building upon the most frequent occurrence. Persist in this until the bothersome doubt disappears, while completely disregarding these waswas and paying them no mind. Also, seek refuge in Allah Almighty through supplication, asking Him to remove this affliction from you.