It is very unlikely that the skin would rupture due to internal bleeding.
Adults have about 5.5 liters of blood inside the circulatory system (arteries/veins/heart/pulmonary circulation) or "intravascular space." When about 40% of blood is lost from the intravascular space (so about 2 liters), the circulatory system collapses, and you die.
Clinical Review: Hemorrhagic Shock (PubMed, 2004):
Intrathoracic injuries, especially to the lung, heart, or the great
vessels, can result in the loss of several liters of blood into the
thorax without external evidence of hemorrhage. Intra-abdominal
injuries to solid organs (spleen and liver) and great vessels
(ruptured aneurysm, penetrating injury to intra-abdominal vessels) can
cause rapid loss of the entire blood volume into the abdomen.
From these examples you can see that internal bleeding does not break the skin.
During deep breathing, your chest volume can increase by 5 liters and nothing breaks. When gas builds in your intestine, the volume of your abdomen can increase by more than 5 liters, which results in obvious abdominal distension, and the skin does not break.
Let's say that a systolic (upper) arterial blood pressure in a healthy adult is about 120 mm Hg. When an artery breaks and the blood escapes into the chest or abdominal cavity, it instantly loses most of the pressure. If the blood accumulates in a cavity and the pressure within it rises to 120 mm Hg, the blood will no longer escape from the arteries and the pressure in a cavity will no longer increase. But the pressure in the chest or abdominal cavity is very unlikely to increase so much just from few liters of blood, because these cavities are quite expandable, mostly due to the diaphragm muscle that can move up or down a lot. I don't know exact pressures in internal bleeding, but, in one case, removal of 4.5 liters of fluid in a patient with ascites, decreased intraabdominal pressure by only 15 mm Hg (from 45 to 30 mm Hg) (ajemjournal.com).
Another comparison: Average see-level atmospheric pressure is 760 mm Hg.
In compartment syndrome (due to bleeding or muscle swelling), the pressure in a limb can increase to as high as 240 mm Hg, but I have never read this would result in skin rupture. Google search for "compartment syndrome" "skin rupture" also does not give any meaningful results.
Somewhat injured skin could break due to a hematoma buildup beneath it, but this is probably not what you are asking.
What happens with the blood in the chest or abdominal cavity? It is slowly decomposed and reabsorbed within weeks/months. Some internal scars (adhesions) may develop as a complication.