hi, dont worry at all about the way you are reacting, you've prob heard it a million times but, everyone copes with things in their own way.
but you've gotta ask yourself, is it actually helping you feel better, or would you rather have the closeness of the ones you love?
you know, it might be worth talking to your doctor about this, its important you are strong for your mum but you are only human... you might find it helpful to get some sort of therepy - they will be able to give you advice on how to deal with things and keep strong, even prescribe sleeping tablets to make sure your getting enough sleep.
i hope you are ok, and your mum... my thoughts are with you and i hope everything turns out ok
Pixie