How do I stop regretting something I genuinely couldn’t control?

I’m a college student struggling badly with anxiety over one subject.
I was genuinely unwell on the day of my college End-Term examination, with severe vomiting, dehydration and weakness. I sought medical attention, submitted my medical documents, followed the required process, and got permission/recommendation for my request.
However, the professor has said there won’t be a re-exam/makeup, and despite emailing to ask how my missed End-Term will be handled, I’m not getting a response. Since the End-Term carries significant weight, I’m now stuck in uncertainty.
I keep thinking, “I should have gone no matter how sick I was. Even if I was on my deathbed, I should have given the exam.” I know that’s irrational because I genuinely wasn’t well, but I can’t stop regretting it or wishing I could go back.
This is affecting my sleep, appetite, concentration, and ability to talk normally. I’ve also had thoughts of self-harm, although I don’t intend to act on them, and I’m planning to see a psychiatrist.
How do I stop punishing myself for something that wasn’t intentional and was genuinely outside my control?