My daughter brought home this cat that is now about 6 months old. She was great at first but then we started noticing that she was missing fur on the side of her stomach. It looked like someone shaved her. Later we saw that she was chewing the fur off herself. Then she went into heat but it seems to be lasting an awful long time. It's been about a month that she has been acting weird. She howls all night and all day and the tone of the howling will change and if you go near her she sticks her rear up and does a strange little dance. I have had cats before who were not fixed and they never did anything like this. They would howl for about a week and it would be over. She won't let you go near her (at first she would) she can come to you but you can't pick her up. I don't know what to do with this cat.

All you can do, aghall, if you want to keep her is get passed this stage of her heat and get her into get fixed and be done with it. Some cats just take longer then others and this is her first heat, so she doesn't know what's going on either.

Tick

Every animal is different. I had at cat that would go into heat and for 3 weeks it would drive me crazy. That's when I had to buckle down and get her fixed. After that she was fine. So I think that when you get her fixed she will stop then you and your daughter can start to enjoy her.

Is it possible she is in pain?
Maybe it hurts to be picked up?
The chewed off fur and crying suggests stress or discomfort.

The first thing you need to do is get her fixed. This is will a lot of problems for you and for her, and she'll live a much healthier life if she is spayed.

Chewing the hair off her side is typically a sign either of a skin condition (has the vet looked at this?) or extreme anxiety or depression. My advice is get her to be spayed and have the vet look at the spot that is hairless then. Getting her spayed will also help with her moods.

If she doesn't have a skin condition (most of which are an easy fix) then it's possible there is something in her environment that is causing her profound distress.