ayse if you have been complained about to HR, you should have been spoken to within a reasonable timescale, and given written confirmation of the outcome, even if it was no action. If this person has told another member of staff that she has complained about you and she hasn't, you have grounds to speak to HR about her! Mediation is available as a way of keeping things informal and finding resolution and agreement about behaviour from now on. Your union will help with giving this and other information if you want to address the problem you have with this person. Have you got a bullying and harrassment policy at work? Unite will be able to proved one for you.
Even if it is workplace incivility and not bullying, it's distressing and should cease. From what you say, it does amount to bullying. As others have advised, keep a record. There is nothing wrong with recording details on the office computer, as you may need to record your log of what's been going on to a manager and/or HR. Just don't access Gransnet on the office computer unless you have specific permission to do so in your break time. Good luck.