Hi mom don't worry. as long as you are feeding your baby your milk, he will not need any water. babies can be exclusively fed on breastmilk for the first 6 months and it actually helps to keep them hydrated and nourished.
if your baby's lips are chapped or cracked, you can take some breastmilk in your finger and apply it over the lips, and gently massage it in. this will also help to keep the lips smooth and soft and heal the cracks.
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