I went to the ER in the dead of night after hours of pain and vomiting, and was admitted, and operated on for a kidney stone. I was scheduled to do a long haul flight in the morning, and called the Chief Pilot from the hospital bed to say I was unavailable. He thanked me for the call and said to give him a holler when I got my medical back.
I didn't understand what that meant at the time, but I did understand that the condition had been completely debilitating. I'd have been unable to perform basic functions in the cockpit, like saying my own name, or counting to two. The pain was unreal, and the constant vomiting and nausea and other signs and symptoms would have prevented any semblance of doing any pilot duties.
I worked through my own AME, and a union AME, and was out for several months. I had a stent put in, three surgeries in total, and a bevy of tests, x-rays, scans, etc, plus a full workup from a urologist, reports, etc...and there was no going back to work until I could show free and clear, no retained stones.
It's not a matter of immediate reporting. When you develop the kidney stone, you're immediately grounded whether you report or not, because you do not meet the conditions for issuance. Any time you have a condition which would prevent issuance, the medical is invalid until you are recovered or over that condition. There are numerous such conditions, however, which require additional documentation to determine that you are "over" the condition. A kidney stone is one of them.
Until you present that data, you are medically unfit and the medical certificate is not valid for use.