Hi gns, I am no expert, but your fear doesn't sound irrational. It might be irrational if your mum had been perfectly healthy, but fighting breast cancer is a pretty big thing.
I think most of us are afraid of losing our parents if we are close to them and I was certainly more afraid of losing my mum than my dad because I was especially close to her. Mums are special, aren't they? After all, we are conceived in and born from their bodies - you can't get much closer than that! I think that in life many of us only experience unconditional love from our mums and our own children.
So I think you should acknowledge your fear as valid, maybe talk to your mum about it, and then try to move on with other thoughts and activities.
When my mum died suddenly and tragically after a lifetime of perfect health, I did feel that I couldn't go on, but I did... It took a long time to learn to live without her and I still often long for her five years later, but I am comforted that I was with her when she died and that I did talk to her about death many times - hers and mine - and she told me that she was not afraid of dying. I have often thought that in our society death is a taboo subject and that we need to find ways of talking about it openly.
I hope that you and your mum both live long and happy lives! X