My one month old baby boy developed a lump right next to his nipple, is this normal?

Can be: Yes, babies can get breast lumps, due to lingering effects of maternal hormones. Ii is not a problem and will resolve, unless it gets red, or hot, or the baby has a fever or acts differently. It may have been smaller at birth and gradually enlarged until noticeable. This is common. See: http://www.webmd.com/parenting/baby/your-newborn-baby-breast-lumps