Tamara Peart, from Bayston Hill, Shrewsbury, has a rare genetic condition called vascular type Ehlers-Danlos Syndrome, which causes fragile blood vessels and intestines which can burst spontaneously.
As a result, the 18-year-old has had dozens of operations that required an amputation and an ileostomy.
Tamara is going on a family holiday next year, and her "big wish" is to go swimming. To do so, she would need a specialist swimming leg which costs about £2,000 and is not on offer on the NHS.
Tamara said her normal prosthetic leg would be too heavy to swim in, and the "swimming leg" would be lighter and designed for the activity.
She also needs a special dry-suit to cover her Hickman line so she can swim.
Surgeon Mark Cheetham launched the fundraising appeal after a meeting with Tamara last week.
Within days donations poured in and the target has been smashed.
For more information visit Mark Cheetham's JustGiving page.