Caveat: I am answering this as an individual who conducts undergraduate student interviews and has been in the workforce for a few years. BUT please keep in mind that I am still a pre-med, so I have no med-based authority.
Although I understand what you are getting at with this example, I think it is weak and would not serve you well. As the reader, I find this example off-putting because, if this is truly one of the most significant challenges you've had to overcome, I am worried that you don't really know what a challenge is or what it is like to fail at something. And if that is the case, then I don't think you have the resilience it takes to get through eight+ more years of arduous training.
A couple ideas of how to think about this question:
Try to think of a time when you failed. Really failed (not just failed a test). Why did you fail? It what ways did overcoming that failure challenge you? What did you not know then that you do now? How has that failure changed you?
Or, try to remember a time when you were thrown way outside your comfort-zone and asked to do something that MANY people would find difficult. Describe the way you approached the situation and in what ways it challenged you. How have you grown from this experience?
And a quick tidbit:
Be honest and show some vulnerability as well as strength, introspection, and growth
EDIT: And don't worry too much about having the "perfect" story that's "unique" enough. Far more important to write something that shows true growth and maturity, even if the example is bland.