Could I be denied entry into Ireland due to medical and police situations during a previous UK visit?

I am an American seeking to enter Ireland for a four-day trip next month. I have documentation for my lodging, funds, and return ticket, so ordinarily I would be fine to enter. However, I have an unusual situation. I was on a trip in the UK (London) that went rather poorly. There are essentially two issues from this past trip that I fear might affect my ability to enter Ireland:

  1. I had to enter the emergency room due to a medical situation. The line to see a doctor was quite long and I left before seeing the doctor. I know they took a photo of my passport at the hospital- I am concerned that (1) my medical information might have been reported to law enforcement/ the border patrol, and (2) that I potentially owe money to the NHS that I am unaware of.
  2. I had a miscommunication with a relative over my travel plans, and was unable to contact them. They filed a missing persons report with the US Embassy and the London police. They later withdrew the missing persons report once I was able to communication with the. I am wary that this past missing persons report will somehow show up when the Irish border runs my passport info.

When I scheduled my trip to Ireland, I was under the impression Ireland was in the Schengen zone. I did not realize that Britain and Ireland share a common immigration system.

My question is – Will these unfortunate incidents from my UK trip potentially affect my ability to enter Ireland?