The Barnes' pediatrician has received very little vaccine, so shortly before Cleo was born, her mother stood in line at a local clinic to get the shot.
"You would expect a doctor's office to get the drugs before you would have to line up in a Home Depot parking lot to get it," said Cleo's dad, Dwayne Barnes.
The Barnes family is part of the Rose City Pediatric Practice in Pasadena.
Dr. Glenn Schlunt says his practice has 10,000 patients. So far they've received 50 doses.
"We have an acute need," said Dr. Schlunt. "There's not enough to go around and the delivery system is highly imperfect."
Dr. Schlunt says he's not alone. In Pasadena, medical providers have received about 13 percent of the H1N1 vaccine. They've ordered a little less than other health departments in California.
On Monday, a person from one doctor's office picked up 30 doses -- a fraction of what they ordered.
The director of Pasadena's Public Health Department says doctors with high risk populations go first.
"We are trying to focus on obstetricians, pediatricians and adult providers that work with some of the high risk groups," said Dr. Takashi Wada.
Children are part of the priority population, but Dr. Wada says the type of vaccine needed for kids is difficult to get.
"The pediatric formulation of the vaccine is scarce," said Dr. Wada. "That's been a challenge for all of us."
The California Department of Health says the state depends on local health officials to decide where to send the vaccine first. Local health officials are expecting more to come in this week.
"I'm hoping that someone from Governor Schwarzenegger's office will see this report and send me some vaccine so that I can take care of my patients," said Dr. Schlunt.
The state, county and Pasadena's Health Department all confirm that new vaccine deliveries are arriving this week and that more providers will be getting more shipments.
They advise patients to continue to call their doctor's offices to find out about their supply.
The Centers for Disease Control and Prevention say there were 27 new lab confirmed swine flu deaths in children under 18. That's the largest one week increase since the new virus was identified in April.