"This is about a two hour wait," said parent Hadley Rierson.
Rierson and her husband both got the H1N1 vaccine from their internist who only had the nasal version. She says he was having a hard time getting rid of it.
However, her 11-month-old daughter, Opal, is too young for the nasal version.
"It is upsetting that those doses aren't going to the pediatricians," said Rierson. "So instead people are having to wait all day in line to get their kids inoculated."
"It's terrible, really terrible," she added.
L.A. County has received 800,000 inoculations, according to Dr. Jeffrey Gunzenhauser, Medical Director for the Department of Public Health in L.A. County. That is only 10 percent of its original order.
About 70 percent of that shipment has gone to health care providers in the private sector. Gunzenhauser says the county tries to make sure that doctors that serve pregnant women and children get them first.
However, many parents say that has not been the case. Because of the shortage, Rierson says she allowed her daughter to get the shot with trace amounts of thimerosal, although that was not her preference.
"Do we give our babies a vaccine with mercury? There has been a big debate about that," said Rierson. "Or do we not vaccinate them at all?"
L.A. County health officials say what they give at clinics is based on what they receive. Limited weekly shipments are forcing the county to make daily changes to their vaccine schedule.
"They are changing almost on a daily basis. So we really encourage individuals who are watching to please follow the news with our Web site," said Marina Alvarez from the L.A. County Department of Health.
A couple of clinics have been canceled and a few more have been added in the area.