I had an oath in Allah's name and I broke it last year. Later, I fasted for two days; since I thought that the ruling is that I must fast for two days when an oath is broken; however, I recently discovered that I should fast for three days instead. Do I have to fast one more day now in order to make up for it?
Just a reminder, a Muslim who broke an oath must either feed or clothe 10 poor people [or free a slave, but nowadays this isn't really an option]. Only when one cannot possibly do those things is when the other option of fasting acceptable. Allah (ﷻ) said:
لا يؤاخذكم الله باللغو في أيمانكم ولكن يؤاخذكم بما عقدتم الأيمان فكفارته إطعام عشرة مساكين من أوسط ما تطعمون أهليكم أو كسوتهم أو تحرير رقبة فمن لم يجد فصيام ثلاثة أيام ذلك كفارة أيمانكم إذا حلفتم واحفظوا أيمانكم كذلك يبين الله لكم آياته لعلكم تشكرون (Allah will not punish you for what is uninentional in your oaths, but He will punish you for your deliberate oaths; for its expiation (a deliberate oath) feed ten Masakin (poor persons), on a scale of the average of that with which you feed your own families; or clothe them; or manumit a slave. But whosoever cannot afford (that), then he should fast for three days.. [Qur'an (5:89)].
As for your question.. "Do i have to fast one more day now in order to make up for it" - Yes, obviously you did not fulfill the obligation and it still sits upon you. And since the scholars say that the 3 fasts must be consecutive (ie, day after day with no breaks in between), then you ought to redo them all. (The first two you already did a while back will just get counted as Nawafil fasts).
Note: Some scholars have a different opinion that the fasts don't have to be consecutive. In their view, you can just offer the 1 day left to fast and that would be sufficient. However, if I were you then I'd pray them all consecutively.. which would involve greater reward for you anyway and also would be on the safe side of both opinions.