✅Answer: Please pay attention to the following narrations:

📚Faqih, Vol. 2, p. 92

1 عَنْ أَبِي جَعْفَرٍ قَالَ: مَنْ صَامَ شَعْبَانَ كَانَ لَهُ طَهُوراً مِنْ كُلِّ زَلَّةٍ وَ وَصْمَةٍ وَ بَادِرَةٍ قَالَ أَبُو حَمْزَةَ لِأَبِي جَعْفَرٍ مَا الْوَصْمَةُ قَالَ الْيَمِينُ فِي الْمَعْصِيَةِ وَ النَّذْرُ فِي مَعْصِيَةٍ قُلْتُ فَمَا الْبَادِرَةُ قَالَ الْيَمِينُ عِنْدَ الْغَضَبِ وَ التَّوْبَةُ مِنْهَا النَّدَمُ عَلَيْهَا

Imam Baqir (peace be upon him) said: 'Whoever fasts the month of Sha'ban, there will be for him purity and cleanliness from every slip, 'wasmah', and 'badirah'.' Abu Hamzah said: 'I asked Imam Baqir (peace be upon him): 'What is 'wasmah'?' He said: 'Swearing in disobedience and vowing in disobedience.' I said: 'What is 'badirah'?' He said: 'Swearing in anger, and its repentance is remorse and regret for it.'

📚Kafi, Vol. 7, p. 442

2 عَبْدِ اللَّهِ بْنِ سِنَانٍ عَنْ أَبِي عَبْداللَّهِ قَالَ: قَالَ: لَا يَمِينَ فِي غَضَبٍ وَ لَا فِي قَطِيعَةِ رَحِمٍ

Translation: Imam Sadiq (peace be upon him) said: 'There is no oath or swearing in a state of anger or about severing ties of kinship.'

'Meaning such an oath is not binding.'

📚Kafi, Vol. 7, p. 444

3 عَنْ سَعِيدٍ الْأَعْرَجِ قَالَ: سَأَلْتُ أَبَا عَبْدِ اللَّهِ عَنِ الرَّجُلِ يَحْلِفُ عَلَى الْيَمِينِ فَيَرَى أَنَّ تَرْكَهَا أَفْضَلُ وَ إِنْ تَرَكَهَا خَشِيَ أَنْ يَأْثَمَ أَ يَتْرُكُهَا قَالَ أَ مَا سَمِعْتَ قَوْلَ رَسُولِ اللَّهِ إِذَا رَأَيْتَ خَيْراً مِنْ يَمِينِكَ فَدَعْهَا

Sa'id said: 'I asked Imam Sadiq (peace be upon him) about a person who makes an oath but sees that leaving that action is better, and if he leaves that action, he fears that he has sinned. Can he leave it?' The Imam said: 'Have you not heard the saying of the Messenger of Allah (peace be upon him and his family): 'When you see something better than your oath, abandon your oath!''

📚Kafi, Vol. 7, p. 443

4 عَنْ عَبْدالرَّحْمَنِ بْنِ أَبِي عَبْداللَّهِ عَنْ أَبِي عَبْداللَّهِ قَالَ: إِذَا حَلَفَ الرَّجُلُ عَلَى شَيْءٍ وَ الَّذِي حَلَفَ عَلَيْهِ إِتْيَانُهُ خَيْرٌ مِنْ تَرْكِهِ فَلْيَأْتِ الَّذِي هُوَ خَيْرٌ وَ لَا كَفَّارَةَ عَلَيْهِ وَ إِنَّمَا ذَلِكَ مِنْ خُطُوَاتِ الشَّيْطَانِ

Imam Sadiq (peace be upon him) said: 'When a person swears an oath about something, and doing something else is better than what he has sworn about, he should do that which is better than his oath, and there is no expiation (kaffarah) on him. Indeed, this is from the steps of Satan.'

📚Kafi, Vol. 7, p. 443

5 عَنْ أَبِي عَبْدِ اللَّهِ قَالَ: مَنْ حَلَفَ عَلَى يَمِينٍ فَرَأَى غَيْرَهَا خَيْراً مِنْهَا فَأَتَى ذَلِكَ فَهُوَ كَفَّارَةُ يَمِينِهِ وَ لَهُ حَسَنَةٌ

Imam Sadiq (peace be upon him) said: 'Whoever swears an oath and sees something other than that action to be better and does it, this will be the expiation for his oath, and it will also be a good deed for him!'

📚Kafi, Vol. 7, p. 449

6 مُحَمَّدِ بْنِ مُسْلِمٍ قَالَ: قُلْتُ لِأَبِي جَعْفَرٍ قَوْلُ اللَّهِ عَزَّ وَ جَلَّ وَ اللَّيْلِ إِذا يَغْشى وَ النَّجْمِ إِذا هَوى وَ مَا أَشْبَهَ ذَلِكَ فَقَالَ إِنَّ لِلَّهِ عَزَّ وَ جَلَّ أَنْ يُقْسِمَ مِنْ خَلْقِهِ بِمَا شَاءَ وَ لَيْسَ لِخَلْقِهِ أَنْ يُقْسِمُوا إِلَّا بِهِ

Muhammad ibn Muslim said: 'I said to Imam Baqir (peace be upon him): 'What is the meaning of God's saying in the Quran: 'By the night when it covers' and 'By the star when it descends' and the like?' The Imam said: 'Indeed, it is for God Almighty to swear by whatever He wishes of His creation, but His creation has no right to swear by anything other than Him.'

📚Tafsir Ayyashi, Vol. 1, p. 74

7 مُحَمَّدِ بْنِ مُسْلِمٍ قَالَ سَمِعْتُ أَبَا جَعْفَرٍ يَقُولُ لا تَتَّبِعُوا خُطُواتِ الشَّيْطانِ قَالَ كُلُّ يَمِينٍ بِغَيْرِ اللَّهِ فَهِيَ مِنْ خُطُوَاتِ الشَّيْطَانِ

Translation: Muhammad ibn Muslim said: 'I heard Imam Baqir (peace be upon him) say about (the verse) 'And do not follow the footsteps of Satan': 'Every oath that is not by God is from the footsteps of Satan.'

✅According to the above narrations and others, an oath by anything other than God and His names is not valid, nor is an oath made in anger binding, nor is anger in disobedience.

Furthermore, even if an oath has all the necessary conditions, but the person who made the oath sees that it is better to leave the action he swore to do, the expiation for this oath is to leave that action, and he will even be rewarded with a good deed!

Therefore, your forgiveness of that person has no problem with respect to the oath you swore.