What happened to Merry after Tom Bombadil saved them from the Barrow-wights?

Question

In the Fellowship of the Ring, chapter "Fog on the Barrow-Downs", the hobbits are captured by the barrow-wights and Tom Bombadil saves them. After Tom wakes them, Merry says something that implies he's possessed or something:

'What in the name of wonder?' began Merry, feeling the golden circlet that had slipped over one eye. Then he stopped, and a shadow came over his face, and he closed his eyes. 'Of course, I remember!' he said. 'The men of Carn Dûm came on us at night, and we were worsted. Ah! the spear in my heart!' He clutched at his breast. 'No! No!' he said, opening his eyes. 'What am I saying? I have been dreaming. Where did you get to, Frodo?'

What happened to Merry? Was he possessed by something? Is this explained anywhere in other books or Tolkien's letters or anywhere?

Answer 1

In layman's terms: Yes, he was possessed and, (speculation); saw a vision of the prince's death.

The tomb in which the Wight imprisoned them was noted to be the grave of the last Cardolan prince.

It was at this time that an end came of the Dunedain of Cardolan, and evil spirits out of Angmar and Rhudaur entered into the deserted mounds and dwelt there.

It is said that the mounds of Tyrn Gorthad, as the Barrowdowns were called of old, are very ancient, and that many were built in the days of the old world of the First Age by the forefathers of the Edain, before they crossed the Blue Mountains into Beleriand, of which Lindon is all that now remains. Those hills were therefore revered by the Dunedain after their return; and there many of their lords and Kings were buried. [Some say that the mound in which the Ring-bearer was imprisoned had been the grave of the last prince of Cardolan, who fell in the war of 1409.]' _{The Lord of the Rings - The Return of the King, Appendix A}

What Merry saw in his sleep were the visions of the late prince, who as fore-mentioned fell in the War.

'The men of Carn Dûm came on us at night, and we were worsted. Ah! the spear in my heart!'

It's likely that Merry experienced the prince's death, in a way. Merry experienced a spear in his heart, likely the cause of the prince's death.

A reference of Armor and the Witch-king is mentioned in The Fellowship of the Ring.

Then he told them that these blades were forged many long years ago by Men of Westernesse: they were foes of the Dark Lord, but they were overcome by the evil king of Carn Dum in the Land of Angmar.

Answer 2

This seems to be a dream caused by the spells of the Barrow-wights

Frodo was the first to "come to" in the Barrow, and he thought the following

“A Barrow-wight had taken him, and he was probably already under the dreadful spells of the Barrow-wights about which whispered tales spoke”.
_{The Fellowship of the Ring: Chapter 8 - Fog on the Barrow Downs}

Although we can't be certain as to the existence of the spells, it seem they may have been what held Frodo under and what was causing Merry's dreams.

These dreams were of days long forgone, when the Witch-King was still in Angmar fighting the Men in the North as described in your quote. These dreams/visions are similar to the ones the Hobbits had when being told a tale of old by Tom Bombadil

vision as it were of a great expanse of years behind them, like a vast shadowy plain over which there strode shapes of Men, tall and grim with bright swords, and last came one with a star on his brow.
_ibid.

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Carn Dûn is the name given to Angmar while the Witch-King ruled. This is mentioned a couple of times in the extended works edited by C.T. Most of the mentions explain the wars between the Men of the North and Carn Dûn. A few times the passage cited in the question is mentioned, but it remains in the form seen above all the way to some of the earliest drafts. Including when Aragon was known as the Hobbit Trotter, and it was Trotter that replaced Frodo as the head of the party of Hobbits.