What is the correct action that pleases Allah in a situation where one's heart is attached to another girl and the fiancée is not accepted, and how can the engagement be annulled without wishing to wrong the fiancée, given the approaching wedding date?

You must repent from engaging in a forbidden emotional relationship. Marriage requires rationality, not mere emotions. Make a good choice based on Islamic principles. You must also perform Istikhara (guidance prayer) and consult others. If a man proposes to a woman and she accepts him, it is not permissible for another to propose to her. If a marriage contract has been concluded with her, then communication with her becomes forbidden. Dissolving an engagement is permissible but disliked without a need.