IT means "she would not allow /did not want anyone to follow her" .The construction is a literary one, rather formal and old fashioned.The structure is "to have someone do something" with no TO.'

Most my answers get down voted although I'm earnestly trying to be helpful =) However even I admit my answers aren't that great. Okay basically the sentence is: After she stop grieving and feeling bad she went to her room alone. She wouldn't let anyone into her room. She wanted to be alone in her room. This sentence is definitely artsy, like I wouldn't say "storm of grief" to a friend unless if I was messing around. In regards to your "TO" question... Let's say all these people want to go into her room and make her feel better. But she's like, no way, stay out. Then there is no TO. But let's say she's in a home by herself. Let's say she's in a house on Mars and there are zero other human beings. Then she would have no one TO follow her. Because there isn't anyone to do the aciton of following her. It's like if I said, "I will have no one follow me to work." That has a nuance that other people want to follow me. Maybe because I smell really good. But if I say "I will have no one to follow me to work" then that has a nuance like nobody wants to follow me anyway. Maybe because I smell really bad. Hope that helps.