Please I want to know If I made an oath in the following situation: I held the quran and promised nobody in particular, I just said "I promise not to do a certain thing" without mentioning Allah or even the quran I was holding. Is it still an oath?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The mere fact of holding the Quran in one’s hand is not considered an oath. Also, your saying: "I promise not to do such and such", is not considered an oath as it does not meet the conditions of the formula of the oath, because it lacks mentioning the name of Allah.

The Maaliki scholar Khaleel said: “The oath is to achieve (fulfill) what is not obligatory by mentioning the Name of Allah or one of His Attributes…..but it [the oath] is not fulfilled by saying ‘you have a covenant upon me (that I will do such and such).’”

Allah knows best.