The child's mother, Lisa Adkinson, said she tried for months to get the swine flu vaccine, but was unsuccessful.
Bella was a high-risk patient who recently survived a brain tumor.
"Why couldn't I do something for my baby? Why, if she was so high risk, and everybody said she had to have it, why couldn't somebody get it for her? She's at risk for any kind of infection, a cold can turn into pneumonia in a matter of hours for her," Adkinson said.
She said she did everything she could to protect her daughter. She kept Bella at home, didn’t allow visitors in her home and even had Bella on waiting lists at six different doctor's offices.
Then on Monday, Bella got a fever. Adkinson took her to the doctor, who gave Bella antibiotics.
"Her fever didn't go away. Wednesday, we took her back, he did a culture, and we were waiting for the results," she said. "By Thursday morning, she was not responding. She wasn't laughing, playing, talking, anything -- she was just laying there."
As she rushed Bella to the hospital, Adkinson finally received the call she had been waiting on for months.
"Evidently, while we were here, her pediatrician did get the shots," Adkinson said.
Adkinson said wished help could have come sooner.
"We did what we were told to do, and it still wasn't enough," she said.
The Adkinsons said Bella's twin brother now has the swine flu vaccine. He's shown no symptoms of the virus. He's also considered high-risk, because he has asthma.
About 22,000 people such as Bella have been hospitalized nationwide in the past month. So far Tarrant County has distributed 3,100 vaccines. Another clinic is planned Thursday. The county has more than 14,000 doses to give out that day.
Ashanti Blaize contributed to this report.