If it's not someone else's "idea", ie you see a news item or, as you have, something on television, and you develop a story around it that is completely fictitious, then you're probably ok. Plagiarism is when you take something someone else has created and copy it - even if not word for word (or note for note with music, say) and pretend it is your own. So if this person you saw has some sort of medical problem, you could use it as your theme.