If I had said "I made a vow to ____", yet this was false and my earlier statement was not an actual vow, does it now become halachically binding by the mere fact that I referred to it as a vow.
The Gemara in Nedarim third perek, deals extensively with numerous cases of vows that are not effective. The underlying rule being, that at the time of the vow, the person fully understood and accepted upon himself the vow.
An example the Gemara (Nedarim 25B, Shavuos 26A) brings is a case of two Amoraim who each swore that Rav meant to say the way they understood it. When they made the vow, they didn’t think it was real because each one believed they were right (similar to your scenario, based on the comments). Upon verification with Rav, even the one who was found to of been mistaken, his vow in annulled since he didn’t really think he was wrong, so he didn’t mean to make a vow.
אמר מר האדם בשבועה פרט לאנוס היכי דמי
The Master says above in the baraita: The phrase “a man…with an oath” serves to exclude a victim of circumstances beyond his control. The Gemara asks: What are such circumstances?
17 כדרב כהנא ורב אסי כי הוו קיימי מקמי דרב מר אמר שבועתא דהכי אמר רב ומר אמר שבועתא דהכי אמר רב כי אתו לקמיה דרב אמר כחד מינייהו אמר ליה אידך ואנא בשיקרא אישתבעי
The Gemara answers: It is as it was with Rav Kahana and Rav Asi, who, when they were standing up in the presence of Rav, their teacher, at the conclusion of a lesson, disagreed with regard to exactly what he said. One Sage said: On my oath Rav said like this, and the other Sage said: On my oath Rav said like that. When they came before Rav to clarify what he had said, he stated his opinion in accordance with what one of them had said. The other said to Rav: Did I then take a false oath?
18 אמר ליה לבך אנסך
Rav said to him: Your heart compelled you. It is not regarded as a false oath, since at the time that you took the oath you were certain that you were telling the truth
There is a principle that a vow or neder is only valid if the person's heart and mouth are on the same subject. See Mishneh Torah Oaths 2 (11, 12)
וְכֵן שְׁאָר מִינֵי שְׁבוּעוֹת אֵינוֹ חַיָּב עַד שֶׁיִּהְיֶה פִּיו וְלִבּוֹ שָׁוִין
and similarly all sorts of vows are not obligatory unless his mouth and heart are equal.
If your earlier statement was not an actual vow, a later change of mind will not constitute פִּיו וְלִבּוֹ שָׁוִין and so your earlier attempt at a vow will not now become halachically binding.