All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If the facts are as you mentioned – that you only made the oath based on the custom that she would reveal to you something concerning her only, and that if you knew that the matter was related to you, you would not have made the oath, then you did not break your oath by divulging this matter. The scholars stated that the reason for one making an oath has an effect on the oath as we have already highlighted in Fatwa 164907. Therefore, an expiation is not required of you for breaking this oath.
If the matter that she disclosed to you leads to spoiling the relationship between you and someone else, then this consists in Nameemah (mischievous gossip) and it is forbidden and the revealed texts warn against it. For more benefit in this regard, please refer to Fatwa 81748and 854420 In the end, she was wrong for conveying that matter to you.
It is not permissible for you to direct accusations against that girl based on what was related to you without evidence. It would be necessary in this situation to seek verification. Allaah says (what means): {O you who have believed, if there comes to you a disobedient one with information, investigate, lest you harm a people out of ignorance and become, over what you have done, regretful.} [Quran 49:6]
If the advantages of investigating this matter are not prevalent, then it would be better to conceal it and anticipate the reward from Allaah.
Please note that what you mentioned in the question about the methods of expiation is not related to the expiation of breaking an oath. To learn about the methods of expiation for breaking oath, please refer to Fatwa 82135. If a person is not able to feed or clothe ten poor people, he must fast for three days.
Allaah Knows best.