Let’s get the obvious question out of the way: Is Shawn Williams really the person in her songs, the one with the messy emotional life? Absolutely, she replies. But not to worry, she’s doing fine.

“Someone told me once that I feel more emotions than anybody else,” she says with a bit of pride. “I remember being in the grocery store when I was 14 and hoping I’d never become the sort of person who gets hard and puts a wal...