You were playing Pokemon Red or Blue, and this is known as the Missingno glitch. This glitch is rather interesting, so I'll include some details on how it works.
Essentially, there was an oversight in the code that made the right edge of Cinnibar Island (where there's the black-ish border) have some unique properties. It counts as a zone where wild Pokemon can spawn, but it also does not specify which Pokemon should spawn there. Because of this, it always uses the Pokemon that were in the last zone that you visited. Thus, it's useful for catching rare Safari Zone Pokemon, because you can battle them for real, putting them to sleep and damaging them, rather than relying on the luck of the Safari Ball.
But that's not enough to explain how Missingno came about. There's more to it. Here's where talking to the Weedle Man comes into play.
When you talk to the man in Viridian City who teaches you how to catch Pokemon by demonstrating on a Weedle, there are some interesting things done with the game's memory state. Pokemon uses all the memory available on the old Game Boy cartridges already. But at this point in the game, it wants the player's name to show as "OLD MAN" rather than whatever the player chose.
In order to do this, it must copy the player's name to an unused portion of memory. Namely: The area where the Pokemon spawn rates for the current zone are stored. Usually this hardly matters, because when you enter a new zone, those values will be overwritten by the ones for the new zone. But if you go straight to Cinnibar Island and ride up and down the coast, some weird things start happening.
Since it doesn't reset which wild Pokemon can spawn, and the last thing in that area of memory was your character's name, not a real spawn table, there are a whole variety of possible outcomes. Pokemon spawn higher than level 100. The Pokemon that spawn are random, depending on the characters in the player's name. And Missingno appears, when there is no real Pokemon corresponding to the data in the table.
The Drake Sword is not recommended in the long run because its damage does not scale with any stats; this means that while it does an awesome 200 damage in the early game, that's not much compared to the damage you can do with high stats and a weapon with good stat scaling.
I personally moved on to Astora's Straight Sword, as recommended by the Wiki; you can find it in The Valley of Drakes, guarded by an undead dragon hanging off the edge of a cliff. If you can pick up two pieces of Twinkling Titianite and upgrade the sword to level 2, it'll already be doing more damage than the Drake Sword* . It's also very forgiving in terms of stats; it scales equally with all of Faith, Dexterity and Strength, so you can make some missteps in your stat distribution without suffering too much for it.
However, as the name implies, it's a straight sword, not a curved sword like you wanted. If that's what you're set on using, the easiest one to get at this point is carried by the merchant Shiva of the East, who is unlocked by joining the Forest Hunter Covenant. He carries the Shotel, which has the nice side-effect of ignoring shields, and a couple of katanas you might want to try out (though they're not curved swords, strictly speaking).
Otherwise, the skeletons in the Catacombs (and not the Firelink Shrine graveyard, unfortunately) sometimes drop Falchions and Scimitars; you'll probably go to the Catacombs soon after Quelaag's Domain, though if you want to you could sneak in there right now.
There's two things to keep in mind when switching, though: these swords scale best with Dexterity, so if you haven't been pumping that stat you might want to start doing so now; also, none of them will do as much damage as your your Drake Sword - although they scale with stats, they start at 82 base damage, compared to the Drake Sword's 200. You probably won't want to switch to one of the curved swords for new areas until you've put some upgrades and practice into it.
If you decide to stick with curved swords throughout the game, I recommend picking a particular one and upgrading it to +10; after that, you can transform it into Quelaag's Furysword, which is one of the best swords in the game.
*The wiki says level 3, but that's the point at which it does more base damage; the scaled damage will eclipse the Drake Sword earlier, though of course this depends on your stats
Best Answer
This is a debug version of the game that was accidentally made public. There's very little information due to it's (illegal?) nature but you can find it floating around. There's a wiki for it: http://darksoulsdebug.wikidot.com/.