No, it isn't necessarily finished, and I hope you and your wife won't start thinking it is. If you assume it's all over you'll quit trying to heal your relationship -- but with God's help the future can be different.
You don't say what causes your bickering; it may be something specific (like money) or something more general. But I suspect it doesn't really matter, because in all likelihood your problem is far deeper than this. And until you face that deeper problem and deal with it, your marriage may continue to flounder.
Let me ask you a question: What is the opposite of love? Is it anger, or hatred, or jealousy, or any of a dozen other negative emotions? These may be involved, of course -- but the opposite of true love can be summarized in one word: selfishness. We want our spouse to meet our needs -- and they want us to meet their needs. But when they don't, we get upset and conflict begins.
This is why I pray that you and your wife will turn to Jesus Christ and ask Him to come into your lives. He can give you a new love for each other -- a love that puts your spouse first instead of yourself. This is the kind of love God has for us -- and it can be yours as you yield your lives to Christ. True love, the Bible says, "is not self-seeking, it is not easily angered, it keeps no record of wrongs" (1 Corinthians 13:5).