An oath does not become binding by merely intending it
Question

Some time ago, I swore to give up something so that I could compel myself to give it up, but I do not remember the details of the oath, whether I swore to give it up for a month or forever? Is it is essential to speak out loud or move the mouth when swearing an oath, because I do not remember whether I spoke it out loud or not?
Praise be to Allah.Firstly: uncertainty about the oath
Uncertainty about an oath is either uncertainty as to whether an oath was sworn in the first place, or uncertainty concerning the details of the oath.
Uncertainty as to whether an oath was sworn in the first place – such as being uncertain as to whether the oath was sworn, or whether it was sworn and broken – in this case, nothing is required of the one who is uncertain, because the basic principle [and what is certain] is that one is under no obligation, and certainty cannot be dispelled by uncertainty.
Ibn Nujaym (may Allah have mercy on him) said: If someone is uncertain as to whether he did something or not, the basic principle is that he has not done it.
End quote from al-Ashbaah wa’n-Nazaa’ir (p. 50).
Secondly: an oath does not become binding merely by thinking about it
Moreover, an oath does not become binding merely by thinking about it; rather it is essential that it be spoken out loud.
As-Sarkhasi (may Allah have mercy on him) said: Merely intending to do something does not mean anything.
End quote from al-Mabsoot (6/76).
An-Nawawi (may Allah have mercy on him) said: Is a vow valid if it is intended, without being spoken? The correct view, according to the consensus of our companions, is that it is not valid unless it is spoken, and intention alone does not mean anything. End quote from al-Majmoo‘ (8/435).
It says in al-Insaaf (11/118): A vow (nadhr) is not valid unless it is spoken out loud. If a person intends it without speaking it, it is not valid, and there is no scholarly difference of opinion concerning that. End quote.
A vow (nadhr) is like an oath (yameen), as the Prophet (blessings and peace of Allah be upon him) said: “A vow is the same as an oath.” Narrated by Ahmad (16889); classed as saheeh by al-Albaani in as-Silsilah as-Saheehah (2860).
The fact that an oath does not become binding by merely intending it is indicated by the report narrated from Abu Hurayrah (may Allah be pleased with him), that the Prophet (blessings and peace of Allah be upon him) said: “Indeed Allah has pardoned my ummah for what crosses their minds, so long as they do not act upon it or speak of it.”
Narrated by al-Bukhaari (5269).
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: This hadith indicates that intention alone does not mean anything, if it is not followed by words or actions.
End quote from Fath al-Baari (9/371).
The scholars of the Permanent Committee for Ifta’ said: If the matter is as you mentioned, that your daughter did not utter the oath or vow out loud – rather she only intended to swear an oath in her heart – then she does not have to do anything, because an oath does not become binding unless it is uttered out loud, swearing by Allah or by one of His attributes, and the like.
End quote from Fatawa al-Lajnah ad-Daa’imah (23/46).
Based on what you mentioned, that you are not certain whether you spoke the oath out loud or not, the basic principle is that you did not swear an oath, therefore you do not have to do anything.
And Allah knows best.