Also, API Triple Sulfa will treat body slime infection, true fungal infections and columnaris. If its fuzzy i think its more likely fungus than body slime. You can try AQ salt at 1tsp per gallon for ten days as a conservative treatment before using actual meds. Clean, warm (78 degree) water is essential, but if he recovers, a larger (2 gallon or bigger) tank is needed. You can purchase thermometers for as cheap as $1.50 and they are pretty important for every tank. Monitor the temp - if you can't get a heater right away, make sure the temp is at least stable. A 1/2 gallon will be extremely hard to find a heater for and heat consistently.
Also, getting him out of the distilled water is a must but you need conditioner in tap water (Seachem Prime is what I recommend) and you need to acclimate him very slowly to the tap water from the distilled because they will have different parameters.
Good luck to you both!