You have to be very careful! I'm guessing this is for your personal statement?
What you have to remember, is so many patients/ family members go through long stays in hospital, due to serious conditions, but not many of them become inspired to pursue the profession.
I can just hear the question now, why do you think that out of all the family members that walk through hospital, you are of a small minority who feel medicine is for them?
if you do manage to make it through to the interview round, you may be seriously probed about your experience, and considering you were 11......
However, the use of personal experiences is certainly a well established form of starting a personal statement, just be aware that it doesnt sound like the sole basis of your decision and that you give evidence for your ambition
Heres another interesting question to reflect about, you said you were inspired at 11, so that means you've had a lot of time to learn about the career,(going on the basis that u must be 17) so what have you done since 11 to substantiate that claim?