Sure. You can definitely use this life experience for a number of essay topics .There is no harm in specifying the name of the medical condition. In fact, without it ,your story would be incomplete. However, instead of going into details of the medical condition, you should focus on your thought process when you got this sad news, how it affected you, how you dealt with (or are still dealing with )this challenge, and how this experience has taught you valuable life lessons.
I don't know which schools you are applying to , but here are a number of essay questions asked by B-schools for which you can use this life -experience effectively:
1."What life event or experience has had greatest influence in shaping your character and why?(UCLA)
2."Describe a circumstance in your life in which you faced adversity, failure or setback. What actions did you take as a result and what did you learn from your experience? (Tuck)
3."Tell us about three setbacks you have faced."(Harvard)
These questions are indicators that schools want to know their potential candidates' ability to deal with adversities bravely, grow and learn from their experiences. In case you are applying to schools that do not require you to write personal questions like these, you may want to share this life experience in your optional essay.
Recently, I had worked with an applicant who had used an experience somewhat similar to yours for the above -mentioned three essay questions as well as for optional essay for some schools. Another applicant I worked with had used her experience of family illness for her optional essay.
I hope it helped.
