If he's spitting up 6 times after one feeding and screaming a lot during the day, I would definitely make an appointment with your pediatrician to discuss reflux. Have you tried elevating the mattress and/or using a baby seat to keep him upright after feeding?
Another suggestion is to find somewhere to weigh your baby before and after a feeding to see how much he's taking in. They did this for moms a breastfeeding group I used to attend, but a lactation consultant, doctor's office, or L&D where you delivered might be able to do this for you. Then if he's getting a really small amount, you know that he's hungry between feedings, and if he's getting a large amount, then it might be reflux discomfort, which could mean that you need smaller, more frequent feedings, or that you can keep going with the bigger feedings at three hours if you take other measures, like keeping him upright or possibly medication, to ease the reflux.
I don't think it's uncommon for reflux pain to start suddenly at a few weeks old rather than being present from birth.