What must a Muslim woman do to rid herself of the blasphemous whisperings that involuntarily come to her mind, and is she considered an infidel because of these whisperings?

What you hear within yourself of insults against Allah, His religion, and His Messenger, may Allah bless him and grant him peace, is from the whispers of Satan. You have no control over it. Allah has forgiven whispers as long as they are not acted upon or spoken, as stated in the Hadith (definition): "Indeed, Allah has forgiven my Ummah for whatever whispers or thoughts cross their minds, as long as they do not act upon them or speak of them." Your dislike and aversion to these thoughts are a sign of the soundness of your belief and the strength of your faith, as stated in the Hadith: "That is pure faith." You must seek refuge with Allah from Satan and desist from these whispers, and increase in supplication and remembrance of Allah, and occupy yourself with what benefits you.