Should 3 months old drink water?

Everyone saying its dangerous and I did avoid giving water at first to avoid water intoxication and also water has no nutrients so why bother to give? But my girl ended up had lots of phelgm and very red lips as she's on formula and had constipation. Ended up I gave abt 10ml a day and gradually increase as she grows bigger and it gotten better. I would say this is very subjective.