I think my ex is stalking me from a fake account.

For the past few weeks, I've been getting ridiculous comments on my posts. I guess it's because my profile isn't private, but all the comments are about my appearance and they're quite snarky. To be honest, I suspect it's my boyfriend's ex-girlfriend because the kid once let it slip that she's a bit obsessive. I mean, when I block her, she literally comes back from another account to harass me. If I went to the police about this, would I get any results, or would you say it's not worth the hassle?