I'm really sorry for your family member and also your anxiety. My lovely dad died from mesothelioma, it is an awful disease,and I too struggle with health anxiety following menopause, so I can completely relate to the panics you get from every little niggle or pain.
I manage to keep on top of my anxiety most of the time (HRT for me, due to her cause of it) but i still have days/weeks of panic if I've had symptoms of cancer which aren't shifting.
What works for me is remembering that, yes, cancer is very common, but mainly in people much older than yourself. I'm in my 50s and still at an age where dying from cancer would be uncommon. The names of people you have mentioned who have sadly died of the disease are known because it is very unusual to die in your 20s of cancer.
Please speak to your GP about your health anxiety. It can be crippling and many people do not appreciate how debilitating it is. And how real it feels, even if you are aware that is what is causing the worry. There are things your GP can do to help you.
You are very young and should be enjoying your life.
All the best to you and your family.