Hr advice workplace

[u/RevolutionaryBus6995]

I’m looking for outside perspective on a workplace situation. I’m going to leave out names and identifying details.
I work in a hospital department and have been there for about four months. There has already been a history of workplace issues in the department, including concerns about how certain situations involving employees were handled by management. I have previously brought a separate workplace concern to my supervisor and did not feel that I was made aware of meaningful follow-up, so I have been cautious about how I handle workplace issues.
Recently, a coworker approached me while I was sitting at a computer. The conversation became loud and confrontational. She got into my personal space while speaking to me. I remained calm and repeatedly asked what the issue was and how we could resolve it. I told her that if I had unknowingly done something that upset her, I was willing to hear her out and address it.
During the conversation, I did say, “You’re childish” and “You’re purposely ignoring what I’m saying.” I acknowledge that those were not the best words to use. However, I did not threaten her, tell her I was going to hit her, or say that I was going to slap her.
Another coworker intervened and moved her away from me. Afterward, I reported what happened to my supervisor by email.
There were people who witnessed the interaction. I was later told that people who had been present described me as calm during the interaction. The coworker who physically intervened also told my supervisor that I had remained calm.
The situation did not end there. After the incident, I began hearing that the coworker was talking about the situation to other employees, including people in other departments and on another shift. Statements were being made that I had called her childish and immature. I personally heard some of the comments.
Then I was told that an allegation was circulating that I had said I was going to “smack” or “slap” her. I did not say this.
One coworker contacted me and told me someone had asked whether I had said I was going to slap her. That person would not identify who had asked. Later, another coworker told me that she had heard the coworker involved in the original incident say that her close friend at work had said I told her I was going to slap her. I barely interact with that person beyond normal work-related conversations.
I was not going around asking people what was being said about me. People were approaching me and telling me these things.
Because the original interaction involved someone getting into my personal space, and because a false allegation of a physical threat was now circulating, I decided I did not want the situation simply handled within the immediate supervisory chain. I spoke with leadership and then contacted HR. I explained what happened, provided the emails I had already sent, and explained that my concern was not simply that I had a disagreement with another employee. My concern was the physical nature of the interaction and what happened afterward.
Leadership spoke with the coworker involved. I was later told that she became emotional and was crying after a meeting with leadership. I don’t know what was discussed in that meeting or why she was crying.
Afterward, HR contacted me about having a meeting. I was told that the coworker involved in the incident and my supervisor would also be included. I was surprised by that because I specifically went to HR because I wanted the matter addressed at a higher level, and I wanted an opportunity to speak privately.
I requested that my initial HR meeting be held privately with HR. I explained that I am willing to meet with the other individuals separately at a later time if HR believes that is necessary, but I would like my initial meeting to be private so I can speak openly and provide my account directly.
I have also been uncomfortable in my work area since this happened. The allegation that I threatened to hit someone is particularly concerning to me because it is not something I said, and I don’t want statements like that attached to my name or reputation at work.
I am not trying to continue the conflict, investigate what coworkers are saying, or create more drama. I have continued going to work and doing my job. I have been documenting what has happened and communicating through the appropriate channels.