How can I fix my newborn's sleep?

There is nothing wrong with your baby's sleep. 1 month olds typically DO NOT sleep through the night. They wake every few hours and need to be fed because their calorie needs are very high and their bellies are still small so eating often is the only way for them to get enough food for them to grow properly. Going to that kind of a schedule can be detrimental to your son. Just feed him on demand - when he is hungry feed him. He knows how much he needs to eat.