How can I know if my spleen is ruptured after falling down stairs?

Go to ER for CT scan. The most sensitive and specific test to diagnose injury to the spleen is a ct of the abdomen. Blunt trauma to the abdomen, like what can occur when falling down stairs, should be taken very seriously. This requires emergency room evaluation.
You may not! This can cause bleeding, abdominal pain, shock and can be delayed sometimes with capsular tear and later leakage. Testing is required to make the diagnosis.