first of all, how many times are you feeding in a day and night please tell me the number of feeding sessions along with the feeding time. Generally, if the baby is sucking the hand and is irritable most of the time at night is because either the baby is not feeeing well or there is not proper burping because of which the baby is irritable. Is the baby gaining weight generally most of the times babies cry at night and are mostly sleeping during the day. This cycle usually resolves by 3 to 4 months.
Next Steps
Try to give at least three feeds at night time and a feeding session should be at least 15 to 20 minutes, followed by burping for 10 to 15 minutes. If you find the baby is not feeling well and is not active or showing any other signs, which are not normal show your nearest pediatrician for physical examination.