Is it legal to deny an employee -- a civil servant -- a promotional opportunity based on a false allegation?

Recently, I interviewed for a promotional opportunity. A few days after the interview, I got a phone call from one of the interviewers who told me I didn't get the promotion because, "you dated that teenage girl." Sorry, never happened. In 2016, a teen informed me that the department supervisor was asking teens if I was having sexual relationships. I requested a meeting with HR and parties involved. I appreciate the concept of conditional privilege. What was HR's response? A non-response. So, I repaired to the EEOC. The EEOC investigated. They found no wrongdoing on my part. But in the EEOC report, the supervisor states there were other "other teens I behaved inappropriately with." So now, this false allegation has added a new level of craziness to the work place. Is it legal? Is it retaliation for going to the EEOC? At this time, at the very least, I would like to hire an attorney to write a letter to my employer summing up the facts and the incident described above.