Unfortunately, that's everything we know about Sting.
Considering the details we do know about it, it's not entirely surprising; Sting is described as a knife, and perfectly-sized for Bilbo:
Bilbo took a knife in a leather sheath. It would have made only a tiny pocket-knife for a troll, but it was as good as a short sword for the hobbit.
The Hobbit Chapter 2: "Roast Mutton"
And as Tom Bombadil points out, Hobbit-sized swords are really only as big as knives for bigger folk:
For each of the hobbits he chose a dagger, long, leaf-shaped, and keen, of marvellous workmanship, damasked with serpent-forms in red and gold. They gleamed as he drew them from their black sheaths, wrought of some strange metal, light and strong, and set with many fiery stones. Whether by some virtue in these sheaths or because of the spell that lay on the mound, the blades seemed untouched by time, unrusted, sharp, glittering in the sun.
'Old knives are long enough as swords for hobbit-people,'
Fellowship of the Ring Book I Chapter 8: "Fog on the Barrow-Downs"
By all accounts Sting was an unremarkable weapon, and whatever history it may have had wasn't considered worth recording.