Does living under grace mean that all my sin that I commit is forgiven by the blood of Jesus Christ?

Does living under grace mean that we no longer worry about our sins since Jesus paid the penalty for our sin? I am a prodigal that came to faith in Christ when I was a boy who hasn't repented yet, but is being moved by the Spirit to no longer be a hedonist. I feel so liberated beacuse I felt like I was living under the Law, and worried about every sin being paid for, but now all I have to do is live according to faith in Christ Jesus.