Itching on the palms and feet at night can be caused by various factors. Some common causes include dry skin, allergies, insect bites, fungal infections, or certain medical conditions like eczema or psoriasis. It is important to identify the underlying cause in order to find an appropriate remedy. If you suspect an allergy or infection, it is advisable to consult a healthcare professional for proper diagnosis and treatment. To alleviate itching, you can try moisturizing your skin regularly, using mild soaps and detergents, avoiding triggers that may worsen symptoms (such as certain fabrics or chemicals), keeping nails short to prevent scratching, and wearing breathable footwear. As for its impact on babies, it is best to consult a pediatrician who can evaluate the specific situation and provide guidance accordingly.