No, you can't fix your DS battery.
As for a replacement, just take out your old battery and look at the mAh and match it. The more mAh the battery has, the longer the battery will last. However, typically when you up mAh the battery size gets bigger (not always) so make sure you have a battery that fits your DS.
I wouldn't buy a used battery because you never know how much life it has left.








