Distilled water can be used for many things. If it is for an iron try a store that sells irons such as Comet or Currys. For a battery try Halfords or your local accessory shop. If it is for first aid, such as eye wash, it must be sterile so try a pharmacist. Once opened they will all keep if the top is screwed on tight, except for the first aid type which must be sterile and once you open it contamination can enter.
Water from a refrigerator is not distilled. You still have all the polution that is in the air and introduced to your fridge when you open the door. In the fridge it is just water vapour from the air that has frozen. Distillation is a science.