A coworker snitched on me. I was then rude to her. What to do?

I have complicated relations with a cowoker. It is like a pendulum, switching from very friendly to hostile due to constant misunderstandings and clash of egos.

Two days ago, I was leaving the job earlier, with authorization from my boss. As I left, she and her boss were smoking outside. Her boss is a "petty tyrant" that like to pester people for the smallest things, and once he bothered me senseless when he saw me leaving earlier. So, I decided to walk fast, to avoid him.

As I am walking by, she spots me, points me to her boss and says: "He is leaving early. Why I also cannot leave early?". Luckly for me, he did not cared, and even if he did, I had authorization from my boss. But what I if didn't? I would have been in serious trouble. Bottonline is: she didn't know if I had authorization to leave or not and pointed to me either way.

Next day, I asked her to talk to me in my room and explained to her that I was bothered by her attitude. She acted nonchalant and sarcastic, as if she had not done anything bad, and did not apologized, so I decided to put her on ice and keep my distance.

She noticied and tried to restart communication with me, as if nothing happened, but this just made me angrier, resulting in me cutting her short in a rather rude manner. I should not have done that, but I dont think her behaviour was acceptable either.

Now we are not talking. Should I apologise, even if she didn't?

A coworker snitched on me. I was then rude to her. What to do?
Post Opinion