It's grammatically possible but vague and somewhat unnatural. A competition makes it sound more complicated than a race, and talking about winning prizes also does. Also, consider whether you mean "I won" or "I have won"
I won my event at the track meet.
I won three races at the track meet.
I won the marathon.
I finished first in my age group in my last 10k.
In high school, I won the prize as my school's best runner. (schools here don't have such a prize, but I can imagine schools somewhere having one)
He's won the 1500m for years, but has never been as successful at longer distances.