If you made a vow, and want to break it, I draw the conclusion that you are not attempting to live by the commandments of Jesus Christ.
If we have not been baptised by immersion into Jesus Christ for the remission of past sins and begun to live a new life by his commandments, then we are not in a covenant relationship with God. We are still dead in trespasses and sins.
Vowing and keeping or breaking vows has no bearing on our salvation if we are not in Christ. We are assured that all sins but one are forgivable in Christ:
Mark 3:28 "Assuredly, I say to you, all sins will be forgiven the sons of men, and whatever blasphemies they may utter…
God is merciful to all that turn from their evil ways and put on Christ in sincerity and truth. After baptism, we cannot live a sinless life. Breaking vows is just another sin to add to our list. Hence the clause in the Lord’s prayer:
Luke 11:4 And forgive us our sins, for we ourselves forgive everyone indebted to us…
John gives us this assurance:
1 John 1:5 This is the message which we have heard from Him and declare to you, that God is light and in Him is no darkness at all. 6 If we say that we have fellowship with Him, and walk in darkness, we lie and do not practice the truth. 7 But if we walk in the light as He is in the light, we have fellowship with one another, and the blood of Jesus Christ His Son cleanses us from all sin. 8 If we say that we have no sin, we deceive ourselves, and the truth is not in us. 9 If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from all unrighteousness.
1 John 1:1 My little children, these things I write to you, so that you may not sin. And if anyone sins, we have an Advocate with the Father, Jesus Christ the righteous. 2 And He Himself is the propitiation for our sins, and not for ours only but also for the whole world. 3 Now by this we know that we know Him, if we keep His commandments. 4 He who says, "I know Him," and does not keep His commandments, is a liar, and the truth is not in him. 5 But whoever keeps His word, truly the love of God is perfected in him. By this we know that we are in Him. 6 He who says he abides in Him ought himself also to walk just as He walked.