I am pursuing a career in radiologic technology because while working at Temple University Hospital, I have had the opportunity to observe multiple radiologic procedures as well as being treated as a patient for a shoulder dislocation.
Having watched someone perform radiology isn't a reason to spend the rest of your life doing it.
The grammar problem here is that almost every sentence begins with the word "I" (and the one that doesn't begins with "my").
Check this out:
I am pursuing a career in radiologic technology because while working at Temple University Hospital, I have had the opportunity to observe multiple radiologic procedures as well as being treated as a patient for a shoulder dislocation. I am very intrigued with how the studies reveal the anatomy and physiology of the human body
While working at Temple University Hospital, I became intrigued with the human anatomy and physiology.