Exaggerated describes something that's been overstated, or described as more impressive than it really is. Your exaggerated details stretched the truth, but they sure made your story funny and memorable.
Something that is exaggerated is described as better or bigger than it actually is, like your exaggerated description of the terrible day you had. Exaggerated can also describe something that is oversized, like the exaggerated collar on a funky sweater. The original meaning of exaggerated, in the early 1500s, was "piled up or accumulated." To spell exaggerate correctly, think of bragger.