@Nancy88,
Backfire is a term that comes from old cars, when the fuel/air ratio was incorrect, the car would make a loud bang sound as it drove down the street.
But in this case it means that the writer made a resolution to see the good in life and found the opposite. Backfire means when you make plans and everything goes awry, failure.
Like planning a wedding in a tropical place and everybody gets sick, a hurricane hits, the ring gets lost... The plan backfired.