Why did Gram have to go to the hospital in Walk Two Moons?

Gram is taken to the hospital in chapter 15 because she has just been bitten by a poisonous snake. The snake is in the Missouri river, where Gram, Gramps, and Sal have been swimming.
Gram feels a pain in her leg and then reaches into the water and brings up a snake, which she thinks is "a water moccasin." She says that the snake has "had a snack" out of her leg. The water moccasin is a species of viper which has a bite that can be fatal.
Gramps cuts a slit in Gram's leg "across the snake bite" so that he can suck the poison out of the wound. Gram is treated at the hospital and spends the night, but is released the next morning with nothing worse than a bit of heatstroke and a bit of shock.