First, let me say all feelings are appropriate. In life we are not responsible for how we feel - only how we act on those feelings.
Second, Cancer changes everything. At the moment you hear the diagnosis your whole future changes. You don't know how, so you are filled with fear, anger, sadness. It is very emotional. But then, you start treatment, and while there are no guarantees, you start planning for your recovery, and it's a different ballgame than the initial shock.
Third, other people's problems don't diminish the significance of your personal concerns to you. I have a pretty good life, in spite of cancer and other personal issues. As a pediatrician I saw lots of problems that made me appreciate my good life even more, but that made me feel like I had no right to complain. Problem is, that kept me from dealing with my own issues, and in the end it didn't help the people who had things worse. So take good care of yourself, including your emotional well being, because your clients need the happy, healthy you to deal with their problems.