How do I prove to him I'm not lying?

[Lyssa]

Alright, so sometimes I tweet to let out some thoughts about how upset I am over one of my friends. And last night I was really upset so I was sort of tweeting towards her. Except, she doesn't follow me on twitter and no one knows who I'm talking about. So my ex, who doesn't have a twitter used his brother's to look at my tweets and believed that one of my tweets about her was actually about him. I tried telling him that it was not for him, it was for someone else and asked him why I would tweet towards him if our relationship and friendship ended months ago and that we were done and over it. He still accused me of lying and said bye. So what do I do? He thinks I'm a filthy liar and now he's made a Twitter too, to probably make sure I am not tweeting about him.