I just completed & repaired the white phial, and I chose healing, and I tested it out but now the phial is "empty" and under miscellaneous. I have tried waiting but it won't refill. Do I need a special item to refill it with or not?
Normally, it should take 24 hours to refill. And you shouldn't need any special items it does it by itself.
However, there is a bug that make break the item:
After the phial refills, the empty phials will remain in your inventory. If you try to delete extra empty phials, the white phial may not refill.