Bedbug bites often appear on sheets, mattresses, bed frames, and nearby baseboards of babies and children. You can check those items for signs of bedbugs if you suspect your baby or child has been bitten.   bedbug bites can be treated with soap and water. Apply a cold compress or over-the-counter anti-itch creams to get additional relief. Cut the baby's nails short so they can't scratch their skin.   Talk to your child's doctor or pharmacist if you want to use steroid creams or oral antihistamines. Some drugs are not safe for babies or young children.   Ask your child not to scratch the bites if he or she is old enough to understand. Your child's nails can also be trimmed and bites covered with a bandage to prevent scratching.