FORT LAUDERDALE (CBSMiami) – Less than a week after setting up a website where people 65 and over can make an appointment to get a COVID-19 vaccination, the state’s health department in Broward has reached its limit.

People going to the department’s website, BrowardCovidVaccine.com, now get the following message.

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“The Florida Department of Health in Broward County has provided 26,465 COVID-19 vaccination appointments to individuals ages 65 and over. All appointments have been filled at this time. Please check back to this website often as more sites and appointments will be added over the coming days and weeks. Thank you.”

After many tries Sunday, Nancy Fishman and her husband, who are from Miami, say they registered to be vaccinated Monday at Vista View Park.

But when they showed up, they were told their names weren’t on the list.

Thankfully, the Fishmans had printed out their confirmation email. And after showing that paperwork, they were given vaccinations.

“My son and daughter-in-law are having a baby in March. I was so happy on Sunday when I got the appointment. I feel like I’ve made it through this,” said Nancy Fishman.

People could begin registering for appointments last Wednesday. The sheer volume of people overwhelmed the website and it crashed. It was brought back online, but the volume of people trying to sign up, forced it to be taken down, and then put back online several times.

The free vaccinations are given by appointment only, no walk-ups allowed. The department said appointments cannot be made by telephone at this time.

Related: What You Need To Know About Getting The COVID-19 Vaccine In South Florida

The first day of the drive-thru vaccinations was Sunday and they were administered at two parks – Vista View Park in Davie and Tradewinds Park in Coconut Creek.

The vaccinations at these two parks are given Sunday through Thursday, 8 a.m. to 4 p.m.

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“It took me two hours to get an appointment,” Noreen Stephens said she waited in line at Vista View Park. “You can’t give up. You have to keep trying and trying.”

While the morning progressed smoothly at the park site, hundreds of people who had appointments were turned away in the afternoon when the site shut down early. The state health department said they would be rescheduled.

Everyone who is vaccinated receives a card with their return appointment for the second and final shot in three weeks. They’re also be monitored briefly to see if there were any bad reactions.

The state health department in Broward said from Sunday to about noon Monday it had vaccinated about 30,000 people.

Vaccinations will also be administered at Markham Park in Sunrise beginning Tuesday, January 5th. Vaccinations will be given Tuesday through Saturday, from 8 a.m. to 4 p.m.

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A fourth site at Holiday Park in Fort Lauderdale is expected to open this week. No hours of operation have been announced

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The state’s health department plans to open more sites in the coming weeks. Broward Mayor Steve Geller said he was told as many as 10 sites could be opened.