Nyad was "really hurting" as she neared her destination of Key West some 48 hours after she set off from Havana, according to blog updates on her website (www.diananyad.com). By early morning on Monday, she was barely 6.5 miles (10.5 km) from completing an estimated 110-mile journey to the Florida Keys.
Nyad surpassed her four previous attempts to make the crossing, setting the record for the longest ocean swim without a shark cage or flippers, according to her crew.
The marathon swimmer has said this would be her final attempt, this time using a protective silicone mask to better protect her from potentially deadly box jellyfish that forced her to end one of two attempted crossings last year.
Her doctors aboard a support vessel said Nyad's tongue and lips were swollen causing her speech to be slurred, and raising concern about her breathing, the blog reported. Nyad was also "very cold" and had cancelled scheduled feeding stops overnight "in the hopes that swimming would keep her warm."
Nyad said at the outset that the custom-made mask slows her and makes it more difficult to breath. Officials initially estimated it could take up to three days to complete the swim, but Nyad was benefiting from a favourable current, her crew members said.
The treacherous Florida Straits has been conquered only once, by Australian Susie Maroney, who used a protective cage at age 22 during a 1997 swim. The cage glided on ocean currents and enabled Maroney to make the journey in just 25 hours.
Australian endurance swimmer Chloe McCardel abandoned her quest in June to make the crossing after she was severely stung by a jellyfish 11 hours into her attempt.
Nyad's fifth attempt to make the crossing comes 35 years after she made her first go at it aged 28 in 1978, when she gave up after covering 76 miles in 42 hours, with the aid that time of a shark cage.
Nyad departed on Saturday morning accompanied by five support boats that also provide her with food and water.
As night fell on Sunday, Nyad put on a jellyfish-protection suit, the website said. She did not immediately use her protective mask. Instead, the exposed parts of her face were slathered with a special protective cream dubbed "Sting Stopper," it said.
At one point on Sunday, the website said, Nyad floated on her back kicking and led a crew of 35 people keeping her on course through the strong Gulf Stream current in singing "Happy Birthday" to a crew member.
"Diana is feeling strong and very coherent," an earlier update read. "She is joking for the first time all day. The only concern is that she is throwing up everything she eats."
Earlier Sunday, Nyad was stopping every 40 minutes to eat, taking several bites of scrambled eggs and pasta, the blog said.
Her long-distance accomplishments include swimming around the island of Manhattan in 1975 and a swim from the Bahamas to Florida in 1979.
(Writing by David Adams and Kevin Gray; Additional reporting by Marc Frank in Havana; Editing by Marguerita Choy)