Does the questioner's statement, "My Lord, protect me from these politicians, and I will not speak again in politics," constitute a vow (nadhr) requiring expiation, and will Allah forgive her sin after she resumed speaking in politics?

You bear no sin for what you uttered, because it is not considered a vow since it does not signify commitment. For a vow to be binding, it must be expressed in words that signify commitment (such as: "It is for Allah upon me to do so-and-so"). And even if we assume it was a vow not to speak about politics, this is a permissible vow that is not binding and does not require expiation.