The problem here is that her complaints to you seem focused on the idea of you dating her boyfriend, not your race or gender. If her boyfriend was seeing a person of a different race than yours, or a guy, the argument here is that her treatment of you would still exist.
As such, this is not likely going to be considered an appropriate EEOC complaint, because the underlying basis of the treatment is relational, not gender or race.
The employer here can also point to this fact and they can point to their prior record of dealing with issues that were based on race alone, which further helps them to state that they are not ignoring your complaints due to any sort of race discrimination.
"Hostile work environment" requires one of those factors to be present, according to the U.S. Supreme Court, so regrettably I do not see you being able to maintain this as a hostile work environment claim unless she outright comes out with racial slurs.
You will, instead, have to focus on the health issues here that this is causing you. Get medical information from your doctor stating that her treatment is contributing to a disability (if you can get an anxiety diagnosis) and then request a "reasonable accommodation" from the employer based on that diagnosis....requiring the harassment to stop. That's the best way forward I can see on these facts.