TL:DR: Although there is no direct modern term or condition relating to "rupturing oneself", an argument can be made for it being used a catch-all diagnosis for sudden death following trauma or intense effort during some lapses of the medieval period.
Before I try to answer your question, we need to address the broadness of the question itself and how this will influence whatever answer we give you.
"Medieval" is a very, very long time period. Roughly from 500 to 1500 CE. In this time medicine advanced greatly but not uniformly. What "rupturing oneself" meant might have changed through time as medicine evolved.
Medieval medicine was very variable. It was not a unified science as it is now. Variations from country to country, region to region and even practitioner to practitioner mean that very different diseases might be referred to with the same name by different people or vice-versa.
With those caveats out of the way let's try to find an answer.
A cursory search does not provide any contemporary examples of "rupturing oneself" or at least not with those exact words. This may be due to a mistranslation or perhaps it is a popular culture trope.
However, the medical term "internal rupture" is used in English sources starting around the year 1000. The death of William I "The Conqueror" is attributed to an "internal rupture" he suffered when he fell off his horse (1) in the siege of Mantes. Henry the IV was said to suffer from "rupture of the internal organs" he lived with this condition for several years and died of an apparently unrelated illness (2). In the case of an inquest of the death of "Richard the Brewer" the coroner reports "internal rupture of the bowels and diaphragm" when he fell while drunk and carrying bag of malt(3).
With this very superficial search (searching for primary sources without a much more detailed timeframe and the location is difficult). It seems that "internal rupture" could mean a variety of pathologies.
You must remember that during that timeframe, physicians did not even have a solid anatomical foundation or a detailed understanding of physiology. And I am not referring to the molecular descriptions of modern medicine but more in line with mistakes in the position of kidneys (one above the other not one right and one left) or that there were two different kinds of blood (this was due to the reliance on Galen's anatomical descriptions which were done on animals and not humans).
So with that in mind, it's easy to see how medieval physicians or even laypeople would refer to something "rupturing" inside the body after a particularly taxing effort such as laughing too hard or eating too many lampreys or simply falling too hard. Since no wounds could be seen from the outside, it is easy to imaging something must have broken on the inside.
Finally, to answer your question: it could be anything. Ranging from internal bleeding from trauma, ruptured aneurysms, pulmonary embolism, ischaemic heart disease, diverticulitis, peptic ulcer disease, etc. In the specific case of Henry the 4th, it seems to refer to rectal prolapse.