The daughter of Reverend John Sheldon, the parish vicar, she was born in Handsworth, West Midlands. She was educated at Handsworth Ladys College and, in 1880, went on to study at Newnham College on a scholarship. She took two Natural Sciences Tripos examinations in 1883 and 1884.
She conducted research on the development of the newt embryo with Alice Johnson and, as well, on the anatomy and morphology of Cynthia rustica now called Styela rustica and Peripatus. Her results were published in the Quarterly Journal of Microscopical Science. Sheldon also contributed a section on Nemertines to volume 2 of the Cambridge Natural History series. She worked at the College as a demonstrator on morphology from 1892 to 1893, and lectured on comparative anatomy from 1893 to 1898. She was a College associate from 1894 to 1906. She retired from academia around 1898.
She later published a number of articles on traditional Devonshire buildings in the Transactions of the Devonshire Association. During World War I, she worked for YMCA in Birmingham, where she was one of the earliest women drivers in the country. She also served on the local hospital committee at Exmouth. Sheldon died there at the age of 80.