After the car accident, the narrator believes that her mother is hurt.
Explanation:
The fear and relief that the narrator experiences after realizing that her mother is unharmed, is followed by her throwing the umbrella away.
This helps the reader know that the umbrella, and what it represents, is no longer important to the narrator.
With the events that happen during the time of the accident, the narrator realizes the extent to which she values her mother and that she doesn't need an umbrella that represents her earlier rejection of her mother.