I find nothing in the Bible that would prevent you from remarrying under these circumstances, if you truly are committed to each other and are willing to overcome whatever problems you had before. The Bible says, "Marriage should be honored by all" (Hebrews 13:4).
Let me, however, make some suggestions as you consider this decision. First, make sure it is God's will for you to remarry, and not only your own desire. Pray about this decision, and ask Him to show you if this is His plan for you. More than that, make Christ the center of your lives -- and your marriage. If you've never done so, ask Him to come into your lives, to forgive the past and give you hope for the future. God gave marriage to us, and He'll give you wisdom and patience for the years ahead.
Then examine honestly what went wrong in the past. Was it simply immaturity? Was it fights over money, or each demanding attention (and not getting it), or hurtful words? Only you can say - but be honest, and ask God to help you overcome these in the future.
Finally, let God's Word, the Bible, be your guide, both as you read it, and as you learn more about it in your church. Above all, discover what true love is by learning about Christ's self-giving love for us. The Bible says, "Love is patient, love is kind.... It does not dishonor others, it is not self-seeking... it keeps no record of wrongs" (1 Corinthians 13:4-5).