“For my sin I admit, I worry about my transgression.” (Psalm 38:19)
The Book of Psalms, indeed, the Bible often uses parallelism – the same idea is expressed in two ways. This is how this verse is usually understood.
Rebbe Nachman of Breslov took it in another direction: David was a master of repentance. He deeply repented for his sins (see Psalm 32 and 51). The sin he’s admitting here is that he worries about past transgressions that he has already repented of. He’s acknowledging that it is wrong to keep beating himself up and obsessing over past errors that God has already forgiven.