It's more than that.
He had, or thought he had, a perfect easy escape in his pocket-- the Ring. All he had to do was put it on, and he was free. He thought of himself running over the grass, grieving for his friends, but free. Too bad for his friends, but "Gandalf would have agreed there was nothing else he could do."
Horrible temptation. And what a horrible thing to live with afterward-- talk about survivor guilt...
What Frodo rejected in the Barrow was his own freedom at the cost of his friends' lives. He decided to stay, and die with them if he could not get them out.
From then on, instead of being consumed by fear, he used his wits. First he thought of using the sword to hack at the hand; then he remembered the song for calling Bombadil.
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...down to the water to see the elves dance and sing upon the midsummer's eve.
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