It's not impossible, but very young people don't have the incidence of cancer as much as older people. Also, if a person is concerned about cancer, they can do sensible things to substantially reduce the chance of ever getting it. Reducing harmful stress, abstaining from tobacco products, eating healthy, exercising, not drinking excessive amounts of alcoholic beverages, and reducing exposure to toxins etc. all lead to a better lifestyle and a much less chance of getting this horrible disease. We see too many people getting this all around us, and we wonder if we will be next. So, it's understandable to have this fear.
In summary, try following a healthy lifestyle, and see your doctor when you are sick and this continues. Start now by reducing your anxiety. I know it's hard because I've been there myself, but I think about the harmful affects that we do to ourselves, so that stops me from going too far.
I hope that helps.