My baby has red pimple like bumps on her arm and leg, they look almost like bug bites. They just appear. What could they be?

Newborn rash. If your baby is a newborn, then it's most likely the common newborn rash erythema toxicum. The rash should clear on its own. No treatment is needed. However, there are similar looking rashes that do need medical attention, so check with your baby's doctor. Here's a link for pic and info: www.Webmd.Com/skin-problems-and-treatments/picture-of-erythema-toxicum-neonatorum.