You're being harassed. If she's no longer singing, it's possible that others found the courage to ask her to stop, once you did. She'd blame that on you; doesn't sound like she takes much responsibility for her own behavior.
About harassment - it isn't just one thing. It's the whole collection of things, over time, and the pattern they form. About harassers - they're very good at convincing everyone else not to see the collection or the pattern. They will admit to one event that looks trivial in isolation and try to make you out to be the problem for "overreacting" to that one event as if it were a one time occurrence. The real issue is that you are having a perfectly valid reaction to that one event times 24/7/365.
IIRC, though, you're working at a churn-and-burn type place. If she's been there for any length of time, she probably has some crony connection to the managers (even if only to one of them). So they aren't going to care about staff turnover, and if she's "got an in" you'll be going long before she does.
I dunno, funkypunky. I know you like the job - but with each thing I learn about your work environment I am asking myself, why *do* you like it at all, at this point? (I'm more sympathetic to you than that may sound.)
Wish I had a good and simply-attained solution for you.
_________________
"I believe you find life such a problem because you think there are the good people and the bad people," said the man. "You're wrong, of course. There are, always and only, the bad people, but some of them are on opposite sides."
-- Terry Pratchett, Guards! Guards!