Is saying, "Oh Lord, I have forsaken such and such," or "I have forsaken so-and-so for Your sake or for Your countenance," considered a vow, a promise, or an oath?

What is mentioned in the question is not considered a vow, due to the absence of a commitment; nor an oath, due to the absence of swearing by Allah or by one of His attributes; nor a covenant, because it is not a pact.