[...] He shut his eyes and struggled for a while; but resistance became unbearable, and at last he slowly drew out the chain, and slipped the Ring on the forefinger of his left hand.
Immediately, though everything else remained as before, dim and dark, the shapes became terribly clear. He was able to see beneath their black wrappings. There were five tall figures: two standing on the lip of the dell, three advancing. In their white faces burned keen and merciless eyes; under their mantles were long grey robes; upon their grey hairs were helms of silver; in their haggard hands were swords of steel. Their eyes fell on him and pierced him, as they rushed towards him. Desperate, he drew his own sword, and it seemed to him that it flickered red, as if it was a firebrand. Two of the figures halted. The third was taller than the others: his hair was long and gleaming and on his helm was a crown. In one hand he held a long sword, and in the other a knife; both the knife and the hand that held it glowed with a pale light. He sprang forward and bore down on Frodo.
The Fellowship of the Ring, Book II, Chapter 11: A Knife in the Dark.
As we see in the excerpt above, when Strider and the Hobbits are camping in Amon Sûl on their way to Imladris, Frodo puts on the One Ring and enters the Unseen World, enabling him to see the real form of the Nazgûl.
Everything seems pretty straightforward and concordant with what happens when an individual enters the Unseen World (e.g., after being stabbed with a Morgul-knife, when Frodo is dying on the East Road, the description of the Nazgûl is identical).
My main issue with this passage is the part where "[Frodo] drew his own sword, and it seemed to him that it flickered red, as if it was a firebrand."
EDIT: As pointed by @A. Giesbrecht, Frodo was using a Barrow-blade given to him (and the other hobbits) by Tom Bombadil after rescuing them in the Barrow-downs.
Sting, as described in Tyler's The Complete Tolkien Companion,
[...] gleamed with a cold blue light if any servants of the Enemy where nigh at hand.
The Complete Tolkien Companion (Second Edition).
However, nothing is mentioned about Sting having a red flickering; I haven't found anything on Foster's Complete Guide to Middle-earth or The Letters of J.R.R. Tolkien either.
Is there any explanation of this red-flickering phenomenon in any of Professor's Tolkien's texts?