If ti is an EEO issue (even a BS one) the agency has a duty to protect the accuser. If they do not protect the accuser, the agency is itself liable to an EEO complaint.
If the ex tells supervision that she is unsafe, or feels unsafe, they will move YOU, not her. By the same token, had you made the accusation, they would have moved her.
The only real way to address it is to file an EEO claim, yourself, probably on harassment by her. State you have been unfairly and unjustifiably targeted by her, and your work assignments now reflect it. She will then have a duty to prove her allegations of you being a threat to her by your previous actions and statements. She will have to provide witnesses or other real proof. Her just "saying so" is not going to be enough for an EEO investigator. All day long they here about a** grabbing, sexual advances, prejudice and all the rest that turn out to be retaliatory, malicious, or otherwise utter nonsense. However, you better come to the EEO table with something better than "the warden makes me work a chow hall every day". You need to be able to prove that your duty posts, or work assignments, are now significantly different and of a completely different pattern than anyone else, and have occurred only since the breakup.
The Agency is awash with bogus and retaliatory EEO claims. The agency knows it. The investigators know it. If, as you imply, it is BS, it should be cut and dry.