Well, it seemed kind of normal for me as my kids are like that too.
My youngest currently 5 months old also like that.
Think mine is worse cos he doesn't even want to lie down on the rocker at all. MUST carry all the time.
Anyway, most babies sleep through the night by five months, but not all. To encourage your baby to get into a regular nighttime sleep rhythm, establish a bedtime routine. Start with a warm bath, followed by a few minutes of gentle rocking with a song and story, and his eyes are sure to start drooping.
Get into the habit of putting your baby into the crib drowsy, rather than fully asleep. This way, he will learn how to soothe himself to sleep rather than relying on you.
During the daytime, your baby will still need two naps -- one in the morning and one after lunch. Try not to delay naps until baby is already tired and cranky. Put him into the crib at the first signs of sleepiness.