My baby has constipation every threw days and i don't know why?

she is 5 months and on similac sensitive lacose free and i have am having to give her sugar water every second day to help her poop. she was on the regular similac when she can home the hospital and she was pooping fine but since at about 1 1/2 months old i found that she was feeling better on the lactose free formula she has been feeling better she has a hard time having a BM. it's like think peanut butter and a few days ago she had such trouble that she ripped her anus a little so that it bled (it has not done it since) but again to today she is having trouble pooping i have started her on some sweet potatoes,and green beans and some prunes to help her go easier but i am not having any success. is there a formula that is lactose free and low iron content ? have any of`you ever had this problem or something similar? any advise would be helpful please!