This is completely normal. I would not put rice in his formula at this age, as they don't reccommend it until much older, but some pediatricians will okay it.
It takes USUALLY several months for a baby to sleep more than four hours at a time. Some babies sleep two hours, wake for one, sleep for two, etc. Many times, though they are hungry when they wake, they may simply want to play or feel secure. If the baby wakes and isn't fussing, or "rooting" for food, just leave him to entertain himself, but don't stimulate him. If he is fussing but doesn't appear hungry, just try to soothe him back to sleep for a little bit before offering food.
I have four kids, and they all followed pretty much this same pattern. It can be exhausting. The best thing you can do is sleep when he sleeps, even during the day, take naps when he is sleeping. You NEED that rest. Also, perhaps, take turns feeding the baby or comforting the baby at night, so you don't become sick with exhaustion. Extra sleep also helps ward off the baby blues/postpartum depression before it starts.
It's okay to need a break. Ask someone to watch the baby for you for a while one day per week so you can have YOU time. And don't use it to go to work, or to clean house, use it for a hot bath, or a walk in the park, or to work on a project you enjoy. Go to the library, where it is nice and quiet. We ALL need quiet time and adult conversaation. Make sure you don't neglect your own needs. You can take care of the baby and still take care of yourself. Trust me. It took me three out of four to figure taht one out.
Good luck and congratulations!