KEY WEST (CBSMiami/AP) — Swollen and sunburned, 64-year-old Diana Nyad is now out of a Key West hospital and all alone in the record books as the only person to swim from Cuba to Florida without a shark cage.

On Tuesday evening, people came out in droves to honor her as she paraded down Duval Street.

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Diana Nyad (L) was honored Tuesday with a parade down Duval Street in her honor. (Ted Scouten/CBS4)

Diana Nyad (L) was honored Tuesday with a parade down Duval Street in her honor. (Ted Scouten/CBS4)

“First we thought it was just going to be a kitschy little thing, but it’s very cool,” an excited Nyad told CBS4’s Ted Scouten. “I mean, people are sincere in their congratulations and the heartfelt things they’re saying.  I’m digging it!”

After some sleep and a few moments to collect her thoughts, Diana had a chance to reflect on realizing a dream, 35 years in the making.

“All my life i don’t know where it came from, I believed in dreaming big. it just doesn’t satisfy me to have small dreams.  I can’t tell you what a big, big dream this is out here.”

Her triumphant trip of more than 100 miles took her about 53 hours.  It was her fifth attempt and came 35 years after her first try.  After swimming ashore, she told the Key West crowd; “never, ever give up.”

Nyad also said she was better-prepared for jellyfish this time because she had a jellyfish expert with her as she made the swim. In addition to a protective suit, she wore a custom-made silicone mask that included a mouthpiece to shield her lips, which have been stung in the past.

“It was rough stuff,” Nyad said during a triumphant Tuesday press conference.

Still, while Nyad was prepared for the jellyfish; the ocean still had a few surprises to throw her way.

“I felt 100 percent prepared for the jellyfish,” Nyad said. “But, every breath when you’re in waves like that, coming through that mask, and I started swallowing, the 13 hours Saturday night, tremendous volumes of sea water.”

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Unfortunately for Nyad, that swallowed seawater brought on a new problem.

“I started vomiting constantly,” Nyad said.

Click here to see photos of Nyad’s swim.

When Nyad arrived in Key West 53 hours after leaving Cuba, she was met by more than a hundred people who were cheering and blowing horns as she made her final approach.

Dazed and sunburned, the athlete waded ashore and promptly received medical help. Nyad’s speech Monday was slurred but she quickly assessed at a local hospital.

Nyad said Tuesday that at some points during her swim she was dealing with delirium and that at one point she thought she saw the Taj Mahal.

Her doctor, Derek Covington of the University of Miami and Jackson Memorial Hospital, said the swimmer was healthy and would not need a long time to recover from dehydration, sunburn and the swelling in and around her mouth.

“She freaking made it,” her website trumped, along with the words “Party time.”

President Barack Obama was among a flurry of public officials and celebrities who tweeted congratulations. The president’s tweet echoed the sentiment Nyad has repeated many times when faced with defeat: “Never give up on your dreams.”

Click video below to watch Jim DeFede’s profile on Diana Nyad in 2010.

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