Most cough and catarrh are viral and will resolve on it's own.
But simple remedies to apply are to exclusively breastfeed, keeping baby warm by avoiding unnecessary bath, once daily is okay. Avoidance of smoke and people with cough and catarrh. No need for medications but if child should develop breathing difficulties kindly take to see a paediatrician.
The treatment of rash depends on the type and cause. Some rashes don't need any treatment while others require different types of treatment. So kindly see a doctor for proper assessment first and possible treatment.
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But simple remedies to apply are to exclusively breastfeed, keeping baby warm by avoiding unnecessary bath, once daily is okay. Avoidance of smoke and people with cough and catarrh. No need for medications but if child should develop breathing difficulties kindly take to see a paediatrician.