I'm under the impression that our life is governed by free will. This being said, I believe that there is good and evil that can grow or shrink within us based on our thoughts and actions. The good seed within us is Christ (selfless love), the evil seed is sometimes referred to as Satan, but Belial (selfish desire) is more appropriate. Just as a plant grows with attention and care, so do these seeds. And if you completely focus on one, the other shrinks and eventually could die.
So how would this lady that felt possessed heal?... The same way that any of us can - Through the Christ within us. Through selfless actions and thoughts. (love)
Now, there is a real possibility of possession, but it involves choosing to take part in actions that could remove your spirit from your soul (even temporarily) and allow another spirit to enter your body. This is not an easy process and usually involves a serious commitment from the person though intentional actions, submissive thoughts, and a very weak Christ within.
If this woman lead a life of selfish action and thought with very little self-less love, then sure, a possession might have occurred. Christ cast out demons (legion for example) and various possessions require various types of commitment, some are as easily released as calling on the name of Christ, but some also require fasting and prayer to heal the person.
I'm under the impression that each day should start with a conscious emptying of your selfish self and asking Christ to fill you with the Holy Spirit and guide you to do God's will.
Then as the day progresses, use this question as your compass as decisions need to be made.
Does this decision lead to a personal gain for my-self?
Yes - feeds your Selfish seed
No - feeds Christ within