When did this fear of losing your mom start? Was it when your parents divorced as well or was that just when the homesickness began? Losing someone in your life is an awfully traumatic event. You don't mention what happened with your father - do you still see him? I only ask because someone doesn't have to die for you to go through a bereavement process (believe me, I know). You will grieve whenever you lose someone in your life even if they simply move far away or stop contacting you suddenly. It is possible that if you don't see your dad any more then you actually went through a grief process there - even if you see him occasionally then you may still have had to grieve to some extent. Your issues concerning the prospect of the loss of your mother may actually be connected to that grief, particularly if you failed to recognise it and deal with it appropriately.
To fear losing someone you are close to is perfectly natural, and of course it is horrible. You have become fixated on the potential loss of your mother though, haven't you? You seem to recognise that this is unhealthy and it is infringing on your ability to function properly as you are getting unnecessarily mad with your mom in order to avoid these feelings. That's a good first step - you see that you have a problem here and that you need to address it. Just asking for help is a great first step to take and it is very brave of you.
One day your mom will pass away, but in the mean time you need to make the most of the time you have together. I'm sure you don't want to think back when this awful thing eventually happens and remember years of fear and unhappiness and fights with your mum to cover up those feelings, do you? That would make you feel terrible wouldn't it? You want to build on your relationship now, and use these feelings of intense love that have for your mom to allow you to be close to each other and enjoy the current time that you have together.
In order to do that though I think you should consider seeking help from a school counsellor or someone regarding your parents divorce. It sounds very much as though you feel abandoned by your father and as though you have a deep seated fear about the loss of people you love in your life as a result - a fear that might well cripple you and your ability to engage in a meaningful relationship with your mother and possibly other loved ones in the future. Counselling could help you to explore those fears, the reasons for them, and ways that you could resolve them and lead a more healthy life again.
Wishing you could die first so you didn't have to live through your mom's death would be horrible for your Mom, who would have to watch her child die - and she sounds like she cares an awful lot for you. She would be terribly unhappy and I'm sure you don't want to do that to her.
There is no need to be ashamed of feeling so insecure, especially about the home-sickness. Many kids who go through divorces experience EXACTLY the same thing - a feeling of intense home sickness that prevents them even from staying with a friend or going on a school trip. At the end of the day these feelings are a product of your own insecurities though and they can be dealt with through therapy and through an exploration of your feelings about your parents, their divorce and the way they treat you.
What you describe is an understandable and treatable reaction, so please do try to seek some help so you can learn to be happy an enjoy your life while you can.