Going up to the neurology department in the local hospital and checking on every patient on the floor compose of my Sundays.
I agree that you don't need that first sentence. However, I also want to point out that if you do use it you should correct it like this:
Going up to the neurology department in the local hospital and checking on every patient on the floor
compose of comprises my Sundays. ----The word is comprise.
You can also say: "My Sundays are composed of trips to the neurology department."
See that difference?
This paragraph IS good enough, because I see how it reflects your good heart and good intentions. YOU are good enough. However, I don't know if the readers will always appreciate how good this idea is. I think you should READ A RECENT JOURNAL ARTICLE that is related to your interests, and mention how you would like to get involved with specific aspects of the field. Show that you are already reading and trying to understand the most modern medical advancements. That will impress readers the most. :-)