Is it normal for my newborn to be feeding all the time?

Yes: Many newborns will feed, on demand, every 1-2 hours, especially if breastfeeding.

Yes: Newborns are wired to suckle 24/7 as a reflex. Try not to confuse the reflex with hunger. Hunger is a learned feeling, a desire to feel better if an emty stomach sends the message. If baby has just eaten, the stomach is not sending that message, but baby may accept a feed for comfort if offered. Breast fed stomachs can empty every 2 hours, formula taked longer. Newborns grow fast and eat often.