What a great question! This gets us to the heart of the Old Testament/New Testament tension. Now that Jesus has come, we struggle to know if the Old Testament is irrelevant, or still applicable for us today.
I think a key to answering this question lies in our understanding of the word "obligated." Many believe that ancient Israel was "obligated" to obey the 10 commandments in order for God to love and accept them. This isn't quite true. God had already declared Abraham, and conversely Israel, righteous because of their faith. God had established a covenant with Israel, and much of the Old Testament law that we read was the parameters of this covenant. In other words, Israel didn't follow the 10 Commandments so that God would find them righteous; they followed the 10 Commandments because God had already declared them righteous. The 10 Commandments taught them how a righteous people would live. So, in this sense, even the people of Israel were not obligated to obey the 10 Commandments- they did so out of their relationship, their covenant, with God.
So, fast forward to the New Testament. Many statements of Jesus and the apostle Paul would suggest that the Old Testament and all its laws have been done away with. We are now under the law of love and the law of Christ. We are free from the Old Testament law! But, and this is key, we are still servants of Christ. If we are following Him, we have submitted our whole lives and our whole selves, all of our actions and activities to Him. We live to please Him. Which brings us to an obvious question- what does it look like to please Christ? How will someone who has devoted their whole selves to Jesus actually live? Ah, now we come to the purpose of the Old Testament in our lives. While the laws and regulations are no longer necessary to forgive sin or make us right with God, these commands do teach us how a Christ-follower will live.
So, when we turn to the Old Testament, and the 10 Commandments, we are no longer looking for a path to peace with God or to personal righteousness. This is only through the blood of Christ. But we do need to ask, "How will a person who loves Jesus express that love in their day to day life?" At this point, instructions such as "Do not lie", "Do not commit adultery", etc., can be tremendously helpful, because in them we come to understand how God views humanity and the world. When we know what is important to Him, we can't help but want to live that way.
You are free...free to do what pleases God. Scripture, the whole thing, offers a great guide for how to do just that. But it is always the relationship, not the laws, that must come first.
May you find incredible joy in that relationship today!