Barrows was first introduced to comics during his childhood when his mother brought home the Brazilian comic, Turma da Monica, created by Mauricio de Sousa. It was then that he developed a love for comics and eventually began to draw. Although he never went to school for art, he studied animation for 2 to 3 years before becoming a full-time artist.
He began his career at 22 years old in Belo Horizonte by doing pictures for school books, children's books, and publicity agencies. Two years later, he began doing tests for Art & Comics Studios. After he was approved, he started his training. His first major assignment was a tie-in comic for the World Wrestling Federation on Stone Cold Steve Austin at Chaos Comics. Afterwards, he took a hiatus from comics because he felt that he needed "more practice".
He returned to comics in 2003, and began doing work for IDW Publishing on G.I. Joe. During this time, his confidence in his art had grown tremendously. He was made the official artist of the book until 2004, when he decided to leave comics to devote more time to a local newspaper. He later returned to Arts & Comics Studios.
After he'd done some art for Avatar Press, he was hired by DC Comics to work on Bloodhound. He went on to work on Batman: Villains Secret Files and Origins, three issues of Birds of Prey, 52, and The All-New Atom. After leaving The Atom, he took over the penciling duties of Teen Titans for a year, and also worked on Action Comics. He has also done various illustrations for the Superman Family titles.
In 2011, as part of DC's relaunch, Barrows will be penciling Nightwing.
Eddy now is doing the art in the Teen Titans ongoing starting with issue 17.