Either your controller isn't properly calibrated, or it became deteriorated due to falling on the ground a lot (for example). The analog mechanism could also be faulty.
If that's the case, it's likely that the analog stick will become inaccurate on its center, causing the player to move erroneously due to the controls. (it was a problem with my other pad and the DsPad plugin for iDeaS, which was way too sensitive)
Anyway, since there's no point playing a DS game with analog controls, you may try slightly moving the analog stick around (so it doesn't glitch that much), and instead use the D-Pad to play the game.
If that's the case, it's likely that the analog stick will become inaccurate on its center, causing the player to move erroneously due to the controls. (it was a problem with my other pad and the DsPad plugin for iDeaS, which was way too sensitive)
Anyway, since there's no point playing a DS game with analog controls, you may try slightly moving the analog stick around (so it doesn't glitch that much), and instead use the D-Pad to play the game.