Is a person considered to have broken an oath of divorce if his father paid the agreed-upon amount on his behalf from his own money, especially if the oath of divorce was made internally and he is unsure whether he uttered it or not?

As long as the matter is merely a thought and you did not utter the oath of divorce, then no divorce occurs by you or your father paying this amount, and nothing is binding upon you. Assuming you did utter the oath, you would not break it by your father paying the money unless your intention was not to pay it yourself. You must be careful not to give in to obsessive thoughts.