Working the Modifier
The wild Pokemon modifier code for "Pokemon HeartGold Version" gives you 493 Master Balls after activating the code and pressing L and R at the same time. You then discard Master Balls until your remaining amount equals the National Pokedex number for the Pokemon you want to catch. Since Swablu is number 333 in the "Pokemon HeartGold" National Pokedex, you'd get rid of 160 Master Balls so you have 333 left, then press L to activate the code. Throwing away any other number of Master Balls will force an encounter with a different Pokemon.
Disable the Code
If you haven't saved your game since this problem started, don't. Saving may make this problem occur for the remainder of your game. Reset and disable the code in the Action Replay menu, then start your game again and see if the problem is resolved. If you've already saved your game, disabling the code is still worth trying.
Change Areas
Try leaving the area you're currently in. For example, enter a nearby building or travel to a different route. While you may be stuck encountering Swablu in the area you first encountered the problem, leaving the area resets the game's programming code you altered while entering the Action Replay code. Test this easily by entering, then exiting the nearest building. Go back to a grassy area and walk around until you encounter a wild Pokemon, which should now be one of the ones you're supposed to encounter.
Restart the Game
If you've tried the other solutions, and you are still stuck encountering Swablu with every wild Pokemon encounter, the best option is to restart your game. Erase your saved file and select "New Game" from the game's menu. While this may not be the answer you want to hear, it's better to start over from scratch and encounter random wild Pokemon, as you're supposed to. Otherwise, you'll be stuck encountering Swablu through the entire game, which won't let you encounter and catch any new Pokemon.