Smell of silk

Bought a new sweater set this week, was pleased, wore it the next day—and then was cross because it reeked of something nasty that gave me a headache, that I hadn't noticed in the store. I figured it was just department store smell, so I washed it today. Twice, even, and it still smells exactly the same. It's a silk, cotton, and rayon blend, and Google tells me that sometimes silk has a distinct smell, but none of the suggestions for removing it seem to be very certain. Anyone have experience with this? I like it, and I doubt I can return it now that I've washed it (twice), but I cannot live with that smell.