But now, the 17-year-old from Mapleton, Utah, says that after college, she'll settle for an indoor career as a lawyer or an economist.
Since age 12, when she broke out in severe hives during a family swim outing, she's been allergic to water.
"I'm just so glad that I didn't take up Olympic swimming," jokes the teen, who will graduate this spring from Springville High School.
"It sounds crazy, I know," she says. "Since the human body is mainly made of water, how could anybody have an allergy to it?"
After her first H2O reaction in 2000, doctors thought Allen might be allergic to chlorine or other harsh chemicals in swimming pools.
So later that summer, when she landed in the hospital after swimming in fresh water in Flaming Gorge, Utah, they were stumped.
"Lexie broke out in an unbearable rash and had bruises on her elbows and knees because she was bleeding into her joints," recalls her father, J. Allen, 53, a business consultant.
"At that point," he says, "we were pretty concerned. It didn't seem to matter what kind of water she came into contact with – chlorinated, hard, soft, fresh or distilled. They all caused a severe reaction."
A Sibling to the RescueIt wasn't until 2013, when her younger brother, Jonah, then 10 (Alexandra is the third of four children), researched his sister's symptoms online, that the family learned about aquagenic urticaria, a rare condition that causes painful or itchy welts to develop when the skin is exposed to water.
"We went in [to her doctor] and said, 'Hey, what about this?' " recalls J. Allen. "It was the only thing that seemed to make sense."
With only 50 cases documented in medical journals worldwide, "it's extremely rare – in fact, I've never seen a case in my practice," says Dr. Barney J. Kenet, a dermatologist at New York-Presbyterian Hospital/Weill Cornell Medical Center who also runs a private practice in Manhattan.
A person who has aquagenic urticaria will typically break out in hives about 20 to 30 minutes after swimming or bathing, he says.
To confirm a diagnosis of the incurable ailment, Allen's dermatologist (who declined to be interviewed for this story) put her through several tests, including having her soak in a warm bath.
"It was excruciating," says Allen, who now takes a cold five-minute shower twice a week, has cut off her long locks to reduce shampoo time and avoids sweating. She has also become a vegetarian to reduce the amount of oil her body produces.
Although experts don't know what causes aquagenic urticaria, Alexandra's symptoms have been somewhat alleviated with shots of Xolair, a medication for chronic hives.
"It's the only thing that's helped – my reactions are about half as bad when I get the shots," she says.
What About Drinking Water?Thus far, Allen hasn't had a problem drinking water, but she says she recently talked to a British woman with the same affliction who now drinks only Diet Coke because her esophagus was affected by the disease as she aged.
"We joked that we'd both found a way to avoid doing dishes," says Allen.
"I'm told that someday, my throat might swell when I drink water, but if there's one thing I've learned since getting this, it's that we all have things to deal with in life," she says.
"I'm hoping that by talking about this weird disease, maybe it will help the next 12-year-old who freaks out because she learns she can't be a mermaid," she says.
J. Allen is proud of his daughter's positive attitude, noting that his entire family has tried to keep a sense of humor about her unusual predicament.
"She is lovely and confident and doesn't let it ruin her life," he says.
"We look at the bright side: Luckily, we live in a fairly dry climate," he says.
Alexandra, who plans to major in economics in college, says that she misses hot showers and swimming, and has given up on her dream of becoming a marine biologist and discovering the world's largest squid.
"But I know that things could be worse," she says. "At least, I'm not allergic to dogs."