@sensiblesometimes, it sounds like you’re in a horrible and unfair situation, I’m so sorry you’re going through this.
My advice would be to write everything down that has been happening, with dates and times, making note of any witnesses present, if there were any. You can either keep this on you, to bring to HR, or future meetings with management, or you can email it to HR/management once you’re comfortable with the wording (worth re-reading a few times to make sure). I would print or forward the emails to your personal address, with any replies, so that you have a record of them. It’s easy to brush aside someone’s complaint when verbal, but it’s harder to ignore them when they’re in black and white and your emails can be used as evidence, should any legal meetings take place in future.
I would also try to separate facts from personal feelings or opinions when talking to management. Of course, you’re emotionally involved, but again it’s harder for people to argue with facts about what happened. When talking to, or emailing management about the situation, you can say that you feel concerned that the person involved may have been told of your complaint, as their behaviour has worsened since you approached management, but that if they have been spoken to, no one has come back to you to confirm that they have and it worries you that things will get worse. Things like that. You can also ask for someone (a colleague, or person outside of your work) to attend meetings with you when you discuss your complaint and you can say this is to help you feel calmer and more supported. However, this can look like you’re taking legal action, so only use this, if you really need someone there with you.
I hope there is light at the end of the tunnel for you and that you’re able to have a positive outcome with either the bully leaving you alone, or being properly dealt with. Remember that outside of work, you can vent to family and friends and freely as you wish, so use them as a sounding board and for support. Good luck and keep us posted.