Welcome to CC, Docgero...
Sorry for your suffering... cancer is all too common. I would make some suggestions, but I'm not a medical doctor, and you didn't come here for medical advice anyway.
To your title question: as you hint, the term "possession" is loaded; some Christians will rail against the possibility, and some will argue the opposite. I try to avoid that (usually very heated) debate by using the words "influence" or "affliction" instead. Demons can definitely influence and afflict Christians; that's why Paul teaches us to put on the full armour of God in Ephesians 6:10-18.
Cancer is definitely a result of the sin of Adam, so ultimately it is not God's will. It is unlikely that this particular case is the will of God, but at the same time He is perfectly able to work within your situation and bring good from it (see Romans 8:28).
Cancer is also specifically a physiological disease, not a "demon", so you can't cast it out as you would a demon. God can heal it though, and He is still in the healing business, so keep praying for that. If I had friends trying to cast out a disease, I'd tell them, "Thanks, but no thanks." You don't need that kind of stress on top of everything else.