Infant Shaking & Shivering in Sleep
Yes, babies do have nightmares. In fact, we know that babies are already dreaming in the womb! Babies are extremely sensitive and pick up on so many levels of information and energy. Yet the processing equipment of their brains is so immature that they can end up with a kind of "psychic indigestion" that can certainly get expressed in distressing dreams. Another contributor can be some kind of trauma the baby has suffered when he was in the womb, during birth or just after. These are times when we tend not to recognize traumas for the kind of impact they have on the baby.
So, what can you do? Hug your baby and hold him. If he isn't really waking and it seems all right, simply be with him, stroking him and crooning softly to him that he is safe in your loving gaze. Chant to him in a way that also calms and soothes you. You might try telling him how very happy you are that he is here with you as your baby son or telling him about the dreams you have for him in his life.
You also should consider what his days are like. Very often, babies and children have to "offgas" overly stimulating days during their sleeping life! See my article, "Keeping Our Children Whole," which discusses the importance of rhythm in the baby's life. Beauty is also helpful for a baby. Silk veils in soft rainbow hues draped over a newborn's cradle or bassinet will soften the sharp contours of this brand new world. Also, keep his food (and yours, if you're still nursing) very simple.
There is so much growth going on at his age; but you don't need to overstimulate your baby to support it.